Laplace Transform for the Solution of Non-Linear Volterra Integral Equation of Second Kind
Abstract
The goal of this work is to solve the second-kind nonlinear Volterra integral problem. The compact form solution of the nonlinear Volterra integral problem of second kind was determined using the Laplace transform. Two numerical problems were investigated, and their solutions were determined in detail using the Laplace transform. The findings of this investigation indicate that the Laplace transform satisfactorily addressed the study's difficulty. By tackling the complexity of Volterra integral equations of the second kind, including their nonlinearity, the Laplace transform opens the way to solving real-world issues in a variety of disciplines.
References
1. Wazwaz, A.M., Linear and Nonlinear Integral Equations: Methods and Applications, Higher Education Press, Beijing, 2011.
2. Jerri, A., Introduction to Integral Equations with Applications, Wiley, New York, 1999.
3. Kanwal, R. P., Linear Integral Equations, Birkhauser, Boston, 1997.
4. Baker, C. T. H., Runge-Kutta methods for Volterra integral equations of the second kind, Lecture Notes in Mathematics 630, Springer-Verlag, Berlin, 1978.
5. Higazy, M., Aggarwal, S. and Taher, A. N., Sawi decomposition method for Volterra integral equation with application, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6687134
6. Aggarwal, S., Dua, A. and Bhatnagar, K., Method of Taylor’s series for the primitive of linear first kind Volterra integral equation, International Journal of Advanced Research, 8(4), 926-931, 2020.
7. Aggarwal, S., Sharma, S.D. and Gupta, A.R., Method of Taylor’s series for the solution of non-linear first kind Volterra integral equations, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(5), 48-52, 2020.
8. Aggarwal, S., Bhatnagar, K. and Dua, A., Method of Taylor’s series for the primitive of linear second kind non-homogeneous Volterra integral equations, International Journal of Research and Innovation in Applied Science, 5(5), 32-35, 2020.
9. Aggarwal, S., Sharma, S.D. and Chaudhary, R., Method of Taylor’s series for non-linear second kind non-homogeneous Volterra integral equations, International Journal of Research and Innovation in Applied Science, 5(5), 40-43, 2020.
10. Jafari, H., A new general integral transform for solving integral equations, Journal of Advanced Research, 32, 133-138, 2021. https://doi.org/10.1016/j.jare.2020.08.016
11. Chauhan R. and Aggarwal, S., Laplace transform for convolution type linear Volterra integral equation of second kind, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 1-7, 2019.
12. Aggarwal, S., Chauhan R. and Sharma, N., A new application of Kamal transform for solving linear Volterra integral equations, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(4), 138-140, 2018.
13. Aggarwal, S., Chauhan R. and Sharma, N., A new application of Mahgoub transform for solving linear Volterra integral equations, Asian Resonance, 7(2), 46-48, 2018.
14. Aggarwal, S., Sharma N. and Chauhan, R., Solution of linear Volterra integral equations of second kind using Mohand transform, International Journal of Research in Advent Technology, 6(11), 3098-3102, 2018.
15. Aggarwal, S., Sharma N. and Chauhan, R., A new application of Aboodh transform for solving linear Volterra integral equations, Asian Resonance, 7(3), 156-158, 2018.
16. Aggarwal, S., Vyas A. and Sharma, S.D., Primitive of second kind linear Volterra integral equation using Shehu transform, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(8), 26-32, 2020.
17. Kumar, A., Bansal S. and Aggarwal, S., A new novel integral transform “Anuj transform” with application, Design Engineering, 2021(9), 12741-12751, 2021.
18. Kumar, R., Chandel J. and Aggarwal, S., A new integral transform “Rishi Transform” with application, Journal of Scientific Research, 14(2), 521-532, 2022. https://dx.doi.org/10.3329/jsr.v14i2.56545
19. Aggarwal, S., Kumar, R. and Chandel, J., Solution of linear Volterra integral equation of second kind via Rishi transform, Journal of Scientific Research, 15(1), 111-119, 2023. https://dx.doi.org/10.3329/jsr.v15i1.60337
20. Aggarwal, S., Kumar, R. and Chandel, J., Exact solution of non-linear Volterra integral equation of first kind using Rishi transform, Bulletin of Pure and Applied Sciences- Math & Stat. 41E(2), Jul-Dec 2022, 159-166, 2022.
21. Aggarwal, S., Gupta, A.R. and Sharma, S.D., A new application of Shehu transform for handling Volterra integral equations of first kind, International Journal of Research in Advent Technology, 7(4), 439-445, 2019.
22. Aggarwal, S., Chauhan, R. and Sharma, N., Application of Elzaki transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(12), 3687-3692, 2018.
23. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Aboodh transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(12), 3745-3753, 2018.
24. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Mahgoub transform for solving linear Volterra integral equations of first kind, Global Journal of Engineering Science and Researches, 5(9), 154-161, 2018.
25. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Kamal transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(8), 2081-2088, 2018.
26. Aggarwal, S. and Sharma, N., Laplace transform for the solution of first kind linear Volterra integral equation, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 16-23, 2019.
27. Upadhyaya, L. M., Introducing the Upadhyaya integral transform, Bulletin of Pure and Applied Sciences, 38E (Math & Stat.) (1), 471-510, 2019. https://doi.org/10.5958/2320-3226.2019.00051.1
28. Higazy M. and Aggarwal, S., Sawi transformation for system of ordinary differential equations with application, Ain Shams Engineering Journal, 12(3), 3173-3182, 2021. https://doi.org/10.1016/j.asej.2021.01.027
29. Higazy, M., Aggarwal S. and Hamed, Y. S., Determination of number of infected cells and concentration of viral particles in plasma during HIV-1 infections using Shehu transform, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6624794
30. Priyanka and Aggarwal, S., Solution of the model of the bacteria growth via Rishi transform, Journal of Advanced Research in Applied Mathematics and Statistics, 7(1&2), 5-11, 2022. https://doi.org/10.24321/2455.7021.202202
31. Aggarwal, S., Gupta, A.R., Singh, D.P., Asthana, N. and Kumar, N., Application of Laplace transform for solving population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9), 141-145, 2018.
32. Aggarwal, S., Kumar, R. and Chandel, J., Rishi transform for determining concentrations of the chemical compounds in first order successive chemical reaction, Journal of Advanced Research in Applied Mathematics and Statistics, 8(1 & 2), 10-17, 2023. https://doi.org/10.24321/2455.7021.202303
33. Sharma, N. and Aggarwal, S., Laplace transform for the solution of Abel’s integral equation, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 8-15, 2019.
34. Aggarwal, S. and Sharma, S.D., Application of Kamal transform for solving Abel’s integral equation, Global Journal of Engineering Science and Researches, 6(3), 82-90, 2019.
35. Aggarwal, S., Sharma, S.D. and Gupta, A.R., A new application of Mohand transform for handling Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(3), 600-608, 2019.
36. Aggarwal, S. and Sharma, S.D., Solution of Abel’s integral equation by Aboodh transform method, Journal of Emerging Technologies and Innovative Research, 6(4), 317-325, 2019.
37. Aggarwal, S. and Gupta, A.R., Sumudu transform for the solution of Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(4), 423-431, 2019.
38. Aggarwal, S. and Gupta, A.R., Shehu transform for solving Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(5), 101-110, 2019.
39. Aggarwal, S. and Bhatnagar, K., Solution of Abel’s integral equation using Sadik transform, Asian Resonance, Vol. 8 No. 2, (Part-1), 57-63, April 2019.
40. Aggarwal, S., Gupta, A.R., Asthana, N. and Singh, D.P., Application of Kamal transform for solving population growth and decay problems, Global Journal of Engineering Science and Researches, 5(9), 254-260, 2018.
41. Aggarwal, S., Pandey, M., Asthana, N., Singh, D.P. and Kumar, A., Application of Mahgoub transform for solving population growth and decay problems, Journal of Computer and Mathematical Sciences, 9(10), 1490-1496, 2018.
42. Aggarwal, S., Sharma, N. and Chauhan, R., Solution of population growth and decay problems by using Mohand transform, International Journal of Research in Advent Technology, 6(11), 3277-3282, 2018.
43. Aggarwal, S., Asthana, N. and Singh, D.P., Solution of population growth and decay problems by using Aboodh transform method, International Journal of Research in Advent Technology, 6(10), 2706-2710, 2018.
44. Aggarwal, S., Singh, D.P., Asthana, N. and Gupta, A.R., Application of Elzaki transform for solving population growth and decay problems, Journal of Emerging Technologies and Innovative Research, 5(9), 281-284, 2018.
45. Aggarwal, S., Sharma, S.D. and Gupta, A.R., Application of Shehu transform for handling growth and decay problems, Global Journal of Engineering Science and Researches, 6(4), 190-198, 2019.
46. Aggarwal, S. and Bhatnagar, K., Sadik transform for handling population growth and decay problems, Journal of Applied Science and Computations, 6(6), 1212-1221, June 2019.
47. Singh, G.P. and Aggarwal, S., Sawi transform for population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 8(8), 157-162, August 2019.
48. Aggarwal, S., Sharma, S.D., Kumar, N. and Vyas, A., Solutions of population growth and decay problems using Sumudu transform, International Journal of Research and Innovation in Applied Science, 5(7), 21-26, 2020.
49. Aggarwal, S., Sharma, N., Chauhan, R., Gupta, A.R. and Khandelwal, A., A new application of Mahgoub transform for solving linear ordinary differential equations with variable coefficients, Journal of Computer and Mathematical Sciences, 9(6), 520-525, 2018.
50. Aggarwal, S. and Chaudhary, R., A comparative study of Mohand and Laplace transforms, Journal of Emerging Technologies and Innovative Research, 6(2), 230-240, 2019.
51. Aggarwal, S., Sharma, N., Chaudhary, R. and Gupta, A.R., A comparative study of Mohand and Kamal transforms, Global Journal of Engineering Science and Researches, 6(2), 113-123, 2019.
52. Aggarwal, S., Mishra, R. and Kumar, A., A comparative study of Mohand and Elzaki transforms, Global Journal of Engineering Science and Researches, 6(2), 203-213, 2019.
53. Aggarwal, S. and Chauhan, R., A comparative study of Mohand and Aboodh transforms, International Journal of Research in Advent Technology, 7(1), 520-529, 2019.
54. Aggarwal, S. and Sharma, S.D., A comparative study of Mohand and Sumudu transforms, Journal of Emerging Technologies and Innovative Research, 6(3), 145-153, 2019.
55. Aggarwal, S., A comparative study of Mohand and Mahgoub transforms, Journal of Advanced Research in Applied Mathematics and Statistics, 4(1), 1-7, 2019.
56. Aggarwal S. and Gupta, A. R., Dualities between Mohand transform and some useful integral transforms, International Journal of Recent Technology and Engineering, 8(3), 843-847, September 2019.
57. Aggarwal S. and Gupta, A. R., Dualities between some useful integral transforms and Sawi transform, International Journal of Recent Technology and Engineering, 8(3), 5978-5982, September 2019.
58. Aggarwal, S., Bhatnagar, K. and Dua, A., Dualities between Elzaki transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 4312-4318, October 2019.
59. Chauhan, R., Kumar, N. and Aggarwal, S., Dualities between Laplace-Carson transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 1654-1659, October 2019.
60. Aggarwal, S. and Bhatnagar, K., Dualities between Laplace transform and some useful integral transforms, International Journal of Engineering and Advanced Technology, 9(1), 936-941, October 2019.
61. Chaudhary, R., Sharma, S. D., Kumar, N. and Aggarwal, S., Connections between Aboodh transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(1), 1465-1470, November 2019.
62. Mishra, R., Aggarwal, S., Chaudhary, L. and Kumar, A., Relationship between Sumudu and some efficient integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(3), 153-159, January 2020.
63. Aggarwal, S., Sharma, N. and Chauhan, R., Duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms, SN Applied Sciences, 2(1), 135, 2020.
64. Malik, S. C. and Arora, S., Mathematical Analysis, New Age International Publishers, New-Delhi, India, 2020.
65. Grewal, B. S., Higher Engineering Mathematics, Khanna Publishers, Delhi, India, 2021.
2. Jerri, A., Introduction to Integral Equations with Applications, Wiley, New York, 1999.
3. Kanwal, R. P., Linear Integral Equations, Birkhauser, Boston, 1997.
4. Baker, C. T. H., Runge-Kutta methods for Volterra integral equations of the second kind, Lecture Notes in Mathematics 630, Springer-Verlag, Berlin, 1978.
5. Higazy, M., Aggarwal, S. and Taher, A. N., Sawi decomposition method for Volterra integral equation with application, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6687134
6. Aggarwal, S., Dua, A. and Bhatnagar, K., Method of Taylor’s series for the primitive of linear first kind Volterra integral equation, International Journal of Advanced Research, 8(4), 926-931, 2020.
7. Aggarwal, S., Sharma, S.D. and Gupta, A.R., Method of Taylor’s series for the solution of non-linear first kind Volterra integral equations, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(5), 48-52, 2020.
8. Aggarwal, S., Bhatnagar, K. and Dua, A., Method of Taylor’s series for the primitive of linear second kind non-homogeneous Volterra integral equations, International Journal of Research and Innovation in Applied Science, 5(5), 32-35, 2020.
9. Aggarwal, S., Sharma, S.D. and Chaudhary, R., Method of Taylor’s series for non-linear second kind non-homogeneous Volterra integral equations, International Journal of Research and Innovation in Applied Science, 5(5), 40-43, 2020.
10. Jafari, H., A new general integral transform for solving integral equations, Journal of Advanced Research, 32, 133-138, 2021. https://doi.org/10.1016/j.jare.2020.08.016
11. Chauhan R. and Aggarwal, S., Laplace transform for convolution type linear Volterra integral equation of second kind, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 1-7, 2019.
12. Aggarwal, S., Chauhan R. and Sharma, N., A new application of Kamal transform for solving linear Volterra integral equations, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(4), 138-140, 2018.
13. Aggarwal, S., Chauhan R. and Sharma, N., A new application of Mahgoub transform for solving linear Volterra integral equations, Asian Resonance, 7(2), 46-48, 2018.
14. Aggarwal, S., Sharma N. and Chauhan, R., Solution of linear Volterra integral equations of second kind using Mohand transform, International Journal of Research in Advent Technology, 6(11), 3098-3102, 2018.
15. Aggarwal, S., Sharma N. and Chauhan, R., A new application of Aboodh transform for solving linear Volterra integral equations, Asian Resonance, 7(3), 156-158, 2018.
16. Aggarwal, S., Vyas A. and Sharma, S.D., Primitive of second kind linear Volterra integral equation using Shehu transform, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(8), 26-32, 2020.
17. Kumar, A., Bansal S. and Aggarwal, S., A new novel integral transform “Anuj transform” with application, Design Engineering, 2021(9), 12741-12751, 2021.
18. Kumar, R., Chandel J. and Aggarwal, S., A new integral transform “Rishi Transform” with application, Journal of Scientific Research, 14(2), 521-532, 2022. https://dx.doi.org/10.3329/jsr.v14i2.56545
19. Aggarwal, S., Kumar, R. and Chandel, J., Solution of linear Volterra integral equation of second kind via Rishi transform, Journal of Scientific Research, 15(1), 111-119, 2023. https://dx.doi.org/10.3329/jsr.v15i1.60337
20. Aggarwal, S., Kumar, R. and Chandel, J., Exact solution of non-linear Volterra integral equation of first kind using Rishi transform, Bulletin of Pure and Applied Sciences- Math & Stat. 41E(2), Jul-Dec 2022, 159-166, 2022.
21. Aggarwal, S., Gupta, A.R. and Sharma, S.D., A new application of Shehu transform for handling Volterra integral equations of first kind, International Journal of Research in Advent Technology, 7(4), 439-445, 2019.
22. Aggarwal, S., Chauhan, R. and Sharma, N., Application of Elzaki transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(12), 3687-3692, 2018.
23. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Aboodh transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(12), 3745-3753, 2018.
24. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Mahgoub transform for solving linear Volterra integral equations of first kind, Global Journal of Engineering Science and Researches, 5(9), 154-161, 2018.
25. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Kamal transform for solving linear Volterra integral equations of first kind, International Journal of Research in Advent Technology, 6(8), 2081-2088, 2018.
26. Aggarwal, S. and Sharma, N., Laplace transform for the solution of first kind linear Volterra integral equation, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 16-23, 2019.
27. Upadhyaya, L. M., Introducing the Upadhyaya integral transform, Bulletin of Pure and Applied Sciences, 38E (Math & Stat.) (1), 471-510, 2019. https://doi.org/10.5958/2320-3226.2019.00051.1
28. Higazy M. and Aggarwal, S., Sawi transformation for system of ordinary differential equations with application, Ain Shams Engineering Journal, 12(3), 3173-3182, 2021. https://doi.org/10.1016/j.asej.2021.01.027
29. Higazy, M., Aggarwal S. and Hamed, Y. S., Determination of number of infected cells and concentration of viral particles in plasma during HIV-1 infections using Shehu transform, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6624794
30. Priyanka and Aggarwal, S., Solution of the model of the bacteria growth via Rishi transform, Journal of Advanced Research in Applied Mathematics and Statistics, 7(1&2), 5-11, 2022. https://doi.org/10.24321/2455.7021.202202
31. Aggarwal, S., Gupta, A.R., Singh, D.P., Asthana, N. and Kumar, N., Application of Laplace transform for solving population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9), 141-145, 2018.
32. Aggarwal, S., Kumar, R. and Chandel, J., Rishi transform for determining concentrations of the chemical compounds in first order successive chemical reaction, Journal of Advanced Research in Applied Mathematics and Statistics, 8(1 & 2), 10-17, 2023. https://doi.org/10.24321/2455.7021.202303
33. Sharma, N. and Aggarwal, S., Laplace transform for the solution of Abel’s integral equation, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 8-15, 2019.
34. Aggarwal, S. and Sharma, S.D., Application of Kamal transform for solving Abel’s integral equation, Global Journal of Engineering Science and Researches, 6(3), 82-90, 2019.
35. Aggarwal, S., Sharma, S.D. and Gupta, A.R., A new application of Mohand transform for handling Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(3), 600-608, 2019.
36. Aggarwal, S. and Sharma, S.D., Solution of Abel’s integral equation by Aboodh transform method, Journal of Emerging Technologies and Innovative Research, 6(4), 317-325, 2019.
37. Aggarwal, S. and Gupta, A.R., Sumudu transform for the solution of Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(4), 423-431, 2019.
38. Aggarwal, S. and Gupta, A.R., Shehu transform for solving Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(5), 101-110, 2019.
39. Aggarwal, S. and Bhatnagar, K., Solution of Abel’s integral equation using Sadik transform, Asian Resonance, Vol. 8 No. 2, (Part-1), 57-63, April 2019.
40. Aggarwal, S., Gupta, A.R., Asthana, N. and Singh, D.P., Application of Kamal transform for solving population growth and decay problems, Global Journal of Engineering Science and Researches, 5(9), 254-260, 2018.
41. Aggarwal, S., Pandey, M., Asthana, N., Singh, D.P. and Kumar, A., Application of Mahgoub transform for solving population growth and decay problems, Journal of Computer and Mathematical Sciences, 9(10), 1490-1496, 2018.
42. Aggarwal, S., Sharma, N. and Chauhan, R., Solution of population growth and decay problems by using Mohand transform, International Journal of Research in Advent Technology, 6(11), 3277-3282, 2018.
43. Aggarwal, S., Asthana, N. and Singh, D.P., Solution of population growth and decay problems by using Aboodh transform method, International Journal of Research in Advent Technology, 6(10), 2706-2710, 2018.
44. Aggarwal, S., Singh, D.P., Asthana, N. and Gupta, A.R., Application of Elzaki transform for solving population growth and decay problems, Journal of Emerging Technologies and Innovative Research, 5(9), 281-284, 2018.
45. Aggarwal, S., Sharma, S.D. and Gupta, A.R., Application of Shehu transform for handling growth and decay problems, Global Journal of Engineering Science and Researches, 6(4), 190-198, 2019.
46. Aggarwal, S. and Bhatnagar, K., Sadik transform for handling population growth and decay problems, Journal of Applied Science and Computations, 6(6), 1212-1221, June 2019.
47. Singh, G.P. and Aggarwal, S., Sawi transform for population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 8(8), 157-162, August 2019.
48. Aggarwal, S., Sharma, S.D., Kumar, N. and Vyas, A., Solutions of population growth and decay problems using Sumudu transform, International Journal of Research and Innovation in Applied Science, 5(7), 21-26, 2020.
49. Aggarwal, S., Sharma, N., Chauhan, R., Gupta, A.R. and Khandelwal, A., A new application of Mahgoub transform for solving linear ordinary differential equations with variable coefficients, Journal of Computer and Mathematical Sciences, 9(6), 520-525, 2018.
50. Aggarwal, S. and Chaudhary, R., A comparative study of Mohand and Laplace transforms, Journal of Emerging Technologies and Innovative Research, 6(2), 230-240, 2019.
51. Aggarwal, S., Sharma, N., Chaudhary, R. and Gupta, A.R., A comparative study of Mohand and Kamal transforms, Global Journal of Engineering Science and Researches, 6(2), 113-123, 2019.
52. Aggarwal, S., Mishra, R. and Kumar, A., A comparative study of Mohand and Elzaki transforms, Global Journal of Engineering Science and Researches, 6(2), 203-213, 2019.
53. Aggarwal, S. and Chauhan, R., A comparative study of Mohand and Aboodh transforms, International Journal of Research in Advent Technology, 7(1), 520-529, 2019.
54. Aggarwal, S. and Sharma, S.D., A comparative study of Mohand and Sumudu transforms, Journal of Emerging Technologies and Innovative Research, 6(3), 145-153, 2019.
55. Aggarwal, S., A comparative study of Mohand and Mahgoub transforms, Journal of Advanced Research in Applied Mathematics and Statistics, 4(1), 1-7, 2019.
56. Aggarwal S. and Gupta, A. R., Dualities between Mohand transform and some useful integral transforms, International Journal of Recent Technology and Engineering, 8(3), 843-847, September 2019.
57. Aggarwal S. and Gupta, A. R., Dualities between some useful integral transforms and Sawi transform, International Journal of Recent Technology and Engineering, 8(3), 5978-5982, September 2019.
58. Aggarwal, S., Bhatnagar, K. and Dua, A., Dualities between Elzaki transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 4312-4318, October 2019.
59. Chauhan, R., Kumar, N. and Aggarwal, S., Dualities between Laplace-Carson transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 1654-1659, October 2019.
60. Aggarwal, S. and Bhatnagar, K., Dualities between Laplace transform and some useful integral transforms, International Journal of Engineering and Advanced Technology, 9(1), 936-941, October 2019.
61. Chaudhary, R., Sharma, S. D., Kumar, N. and Aggarwal, S., Connections between Aboodh transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(1), 1465-1470, November 2019.
62. Mishra, R., Aggarwal, S., Chaudhary, L. and Kumar, A., Relationship between Sumudu and some efficient integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(3), 153-159, January 2020.
63. Aggarwal, S., Sharma, N. and Chauhan, R., Duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms, SN Applied Sciences, 2(1), 135, 2020.
64. Malik, S. C. and Arora, S., Mathematical Analysis, New Age International Publishers, New-Delhi, India, 2020.
65. Grewal, B. S., Higher Engineering Mathematics, Khanna Publishers, Delhi, India, 2021.
Published
2023-11-30
How to Cite
AGGARWAL, Sudhanshu; VYAS, Aakansha.
Laplace Transform for the Solution of Non-Linear Volterra Integral Equation of Second Kind.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 8, n. 3&4, p. 18-25, nov. 2023.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/929>. Date accessed: 08 sep. 2024.
Section
Research Article
