Kamal Transform for Addressing the Problem of Non-Linear Volterra Integral Equation of Second Kind
Abstract
Solving the second-kind nonlinear Volterra integral equation is the aim of this effort. The Kamal transform was used to find the compact form solution of the nonlinear Volterra integral problem of second class. A pair of numerical issues was examined, and the Kamal transform was utilized to ascertain their precise solutions. The investigation’s conclusions show that the Kamal transform adequately solved the study’s challenge. The Kamal transform tackles the nonlinearity and complexity of Volterra integral equations of the second kind, paving the path for practical solutions across multiple fields.
References
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14. 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.
15. Kumar, A., Bansal S. and Aggarwal, S., A new novel integral transform “Anuj transform” with application, Design Engineering, 2021(9), 12741-12751, 2021.
16. 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
17. 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
18. 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
19. 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
20. 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
21. Kumar, A., Bansal, S. and Aggarwal, S., Determination of the concentrations of the reactants of first order consecutive chemical reaction using Anuj transform, European Chemical Bulletin, 12(7), 2528-2534, 2023.
22. Kumar, A., Bansal, S. and Aggarwal, S., Determination of the blood glucose concentration of a patient during continuous intravenous injection using Anuj transform, Neuroquantology, 19(12), 303-306, 2021.
23. 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.
24. 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. https://doi.org/10.1007/s42452-019-1896-z
25. Malik, S. C. and Arora, S., Mathematical Analysis, New Age International Publishers, New-Delhi, India, 2020.
26. Grewal, B. S., Higher Engineering Mathematics, Khanna Publishers, Delhi, India, 2021.
2. Kanwal, R. P., Linear Integral Equations, Birkhauser, Boston, 1997.
3. Jerri, A., Introduction to Integral Equations with Applications, Wiley, New York, 1999.
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., 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.
7. 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.
8. 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
9. 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.
10. 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.
11. 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
12. 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
13. 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. https://doi.org/10.5958/2320-3226.2022.00022.4
14. 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.
15. Kumar, A., Bansal S. and Aggarwal, S., A new novel integral transform “Anuj transform” with application, Design Engineering, 2021(9), 12741-12751, 2021.
16. 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
17. 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
18. 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
19. 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
20. 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
21. Kumar, A., Bansal, S. and Aggarwal, S., Determination of the concentrations of the reactants of first order consecutive chemical reaction using Anuj transform, European Chemical Bulletin, 12(7), 2528-2534, 2023.
22. Kumar, A., Bansal, S. and Aggarwal, S., Determination of the blood glucose concentration of a patient during continuous intravenous injection using Anuj transform, Neuroquantology, 19(12), 303-306, 2021.
23. 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.
24. 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. https://doi.org/10.1007/s42452-019-1896-z
25. Malik, S. C. and Arora, S., Mathematical Analysis, New Age International Publishers, New-Delhi, India, 2020.
26. Grewal, B. S., Higher Engineering Mathematics, Khanna Publishers, Delhi, India, 2021.
Published
2024-06-27
How to Cite
AGGARWAL, Sudhanshu et al.
Kamal Transform for Addressing the Problem of Non-Linear Volterra Integral Equation of Second Kind.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 9, n. 1&2, p. 22-28, june 2024.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/1178>. Date accessed: 18 oct. 2024.
Section
Research Article
