Rishi Transform of Bessel Functions of First Kind
Abstract
Various problems of Statistics, Mathematics, Radio Physics, Nuclear Physics, Atomic Physics, Fluid Mechanics, Engineering and Science can easily handle by applying integral transform techniques on their mathematical models. Problems of heat equation, wave equation, Laplace equation, Helmholtz equation and Schrodinger equation have solutions in terms of Bessel functions. To solve such equations by integral transform methods, we need to know the integral transform of Bessel functions. In this paper, authors determine the Rishi transform of Bessel functions of first kind of orders zero, one and two.
References
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36. 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.
37. 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. http://dx.doi.org/10.3329/jsr.v15i1.60337
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39. 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, Section-E-Mathematics & Statistics, 41E(2), 159-166, 2022.
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43. Aggarwal, S. and Gupta, A.R., Solution of linear Volterra integro-differential equations of second kind using Kamal transform, Journal of Emerging Technologies and Innovative Research, 6(1), 741-747, 2019.
44. Aggarwal, S., Sharma, S.D. and Vyas, A., Solution of convolution type Volterra integro-differential equation of first kind using Kamal transformation, International Journal of Research and Innovation in Applied Science, 5 (7), 137-143, 2020.
45. Aggarwal, S., Sharma, N. and Chauhan, R., Solution of linear Volterra integro-differential equations of second kind using Mahgoub transform, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(5), 173-176, 2018.
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47. Aggarwal, S., Sharma, S.D. and Vyas, A., Aboodh transform for solving first kind faltung type Volterra integro-differential equation, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(7), 71-77, 2020.
48. Aggarwal, S., Gupta, A.R. and Sharma, S.D., Application of Sadik transform for handling linear Volterra integro-differential equations of second kind, Universal Review, 10(7), 177-187, July 2019.
49. Aggarwal, S., Vyas, A. and Sharma, S.D., Analytical solution of first kind Volterra integro-differential equation using Sadik transform, International Journal of Research and Innovation in Applied Science, 5(8), 73-80, 2020.
50. Aggarwal, S., Vyas, A. and Sharma, S.D., Mohand transform for handling convolution type Volterra integro-differential equation of first kind, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(7), 78-84, 2020.
51. Aggarwal, S., Vyas, A. and Sharma, S.D., Primitive of faltung type Volterra integro-differential equation of first kind using Elzaki transform, International Journal of Research and Innovation in Applied Science, 5(7), 144-150, 2020.
52. Aggarwal, S., Sharma, S.D. and Vyas, A., Laplace-Carson transform for the primitive of convolution type Volterra integro-differential equation of first kind, International Journal of Research and Innovation in Applied Science, 5(7), 30-36, 2020.
53. Aggarwal, S., Sharma, S.D. and Vyas, A., Laplace transformation for the solution of faltung type Volterra integro-differential equation of first kind, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(7), 5-11, 2020.
54. Aggarwal, S., Sharma, S.D. and Vyas, A., Application of Sawi transform for solving convolution type Volterra integro-differential equation of first kind, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(8), 13-19, 2020.
55. Aggarwal, S., Sharma, S.D. and Vyas, A., Application of Sumudu transform for handling Volterra integro-differential equation of first kind with convolution kernel, International Journal of Research and Innovation in Applied Science, 5(8), 24-30, 2020.
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59. 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.
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2. Jerri, A., Introduction to integral equations with applications, Wiley, New York, 1999.
3. 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
4. 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
5. Aggarwal, S., Kumar, R. and Chandel, J., Rishi transform for determining the 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
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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.
22. S. Maitama and W. Zhao, New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations, International Journal of Analysis and Applications, 17(2), 167-190, 2019. https://doi.org/10.1186/s13662-019-2068-6
23. 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
24. Ahmed, S.A., Elzaki, T.M., Elbadri, M. and Mohamed, M.Z., Solution of partial differential equations by new double integral transform (Laplace-Sumudu transform), Ain Shams Engineering Journal, 12(2021), 4045-4049. https://doi.org/10.1016/j.asej.2021.02.032
25. 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.
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. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. 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.
33. 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.
34. 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.
35. 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.
36. 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.
37. 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. http://dx.doi.org/10.3329/jsr.v15i1.60337
38. Kumar, R., Chandel, J. and Aggarwal, S., A new integral transform “Rishi Transform” with application, Journal of Scientific Research, 14(2), 521-532, 2022. http://dx.doi.org/10.3329/jsr.v14i2.56545
39. 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, Section-E-Mathematics & Statistics, 41E(2), 159-166, 2022.
40. Aggarwal, S., Kumar, R. and Chandel, J., Application of Rishi transform to the solution of nonlinear Volterra integral equation of the second kind, Bulletin of Pure and Applied Sciences, Section-E-Mathematics & Statistics, 42E(2), 186-193, 2023.
41. Jafari, H. and Aggarwal, S., Upadhyaya integral transform: A tool for solving non-linear Volterra integral equations, Mathematics and Computational Sciences, 5(2), 63-71, 2024. https://doi.org/10.30511/MCS.2024.2029301.1174
42. 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
43. Aggarwal, S. and Gupta, A.R., Solution of linear Volterra integro-differential equations of second kind using Kamal transform, Journal of Emerging Technologies and Innovative Research, 6(1), 741-747, 2019.
44. Aggarwal, S., Sharma, S.D. and Vyas, A., Solution of convolution type Volterra integro-differential equation of first kind using Kamal transformation, International Journal of Research and Innovation in Applied Science, 5 (7), 137-143, 2020.
45. Aggarwal, S., Sharma, N. and Chauhan, R., Solution of linear Volterra integro-differential equations of second kind using Mahgoub transform, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(5), 173-176, 2018.
46. Aggarwal, S., Sharma, N. and Chauhan, R., Application of Aboodh transform for solving linear Volterra integro-differential equations of second kind, International Journal of Research in Advent Technology, 6(6), 1186-1190, 2018.
47. Aggarwal, S., Sharma, S.D. and Vyas, A., Aboodh transform for solving first kind faltung type Volterra integro-differential equation, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(7), 71-77, 2020.
48. Aggarwal, S., Gupta, A.R. and Sharma, S.D., Application of Sadik transform for handling linear Volterra integro-differential equations of second kind, Universal Review, 10(7), 177-187, July 2019.
49. Aggarwal, S., Vyas, A. and Sharma, S.D., Analytical solution of first kind Volterra integro-differential equation using Sadik transform, International Journal of Research and Innovation in Applied Science, 5(8), 73-80, 2020.
50. Aggarwal, S., Vyas, A. and Sharma, S.D., Mohand transform for handling convolution type Volterra integro-differential equation of first kind, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(7), 78-84, 2020.
51. Aggarwal, S., Vyas, A. and Sharma, S.D., Primitive of faltung type Volterra integro-differential equation of first kind using Elzaki transform, International Journal of Research and Innovation in Applied Science, 5(7), 144-150, 2020.
52. Aggarwal, S., Sharma, S.D. and Vyas, A., Laplace-Carson transform for the primitive of convolution type Volterra integro-differential equation of first kind, International Journal of Research and Innovation in Applied Science, 5(7), 30-36, 2020.
53. Aggarwal, S., Sharma, S.D. and Vyas, A., Laplace transformation for the solution of faltung type Volterra integro-differential equation of first kind, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(7), 5-11, 2020.
54. Aggarwal, S., Sharma, S.D. and Vyas, A., Application of Sawi transform for solving convolution type Volterra integro-differential equation of first kind, International Journal of Latest Technology in Engineering, Management & Applied Science, 9(8), 13-19, 2020.
55. Aggarwal, S., Sharma, S.D. and Vyas, A., Application of Sumudu transform for handling Volterra integro-differential equation of first kind with convolution kernel, International Journal of Research and Innovation in Applied Science, 5(8), 24-30, 2020.
56. Aggarwal, S., Vyas, A. and Sharma, S.D., Primitive of first kind Volterra integro-differential equation using Shehu transform, International Journal of Research and Innovation in Applied Science, 5(8), 31-38, 2020.
57. 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.
58. 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.
59. 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.
60. 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.
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Published
2024-11-27
How to Cite
AGGARWAL, Sudhanshu; KUMAR, Rishi; CHANDEL, Jyotsna.
Rishi Transform of Bessel Functions of First Kind.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 9, n. 3&4, p. 32-42, nov. 2024.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/1330>. Date accessed: 21 dec. 2024.
Section
Research Article
