Solution of Fractional Kinetic Equations Involving generalized q−Bessel function

Yıl 2022, , 87 - 95, 31.03.2022

D. D. Pawar , Wagdi F. Ahmed

https://doi.org/10.53006/rna.1009728

Cited By: 1

Öz

In this article, we pursue and examine the solutions to fractional
kinetic equations that incorporate the q−Bessel function through their Sumudu
transformations. An important special case is revealed in the process. The
results obtained with the q− Bessel function are quite general in nature and
can easily set up different new and known fractional kinetic equations.

Anahtar Kelimeler

Fractional kinetic equation, Generalized Mittag-Leffler function, q−Bessel function, and Sumudu Transform.

Kaynakça

• [1] P. Agarwal, S.K. Ntouyas, S. Jain, M. Chand, and G. Singh. Fractional kinetic equations involving generalized k-Bessel function via Sumudu transform. Alexandria Eng.J., 2017
• [2] W.F.S. Ahmed, D.D. Pawar, and W.D. Patil Fractional kinetic equations involving generalized V−function via Laplace transform. Advances in Mathematics: Scientific 10 (2021), no.5,2593−2610
• [3] W.F.S. Ahmed and D.D. Pawar, Application of Sumudu Transform on Fractional Kinetic Equation Pertaining to the Generalized k-Wright Function. Advances in Mathematics: Scientific Journal 9 (2020), no.10, 8091- 8103
• [4] M. Chand, R. Kumar, and S. Bir Singh Certain Fractional Kinetic Equations Involving Product of Generalized k-Wright function Bulletin of the Marathwada Mathematical Society Vol. 20, No.1, June 2019, Pages 22-32
• [5] M. Chand, et al. Certain fractional integrals and solutions of fractional kinetic equations involving the product of S-function. Mathematical Methods in Engineering. Springer, Cham, 2019. 213-244.
• [6] V. B. L. Chaurasia and D. Kumar On the Solutions of Generalized Fractional Kinetic Equations. Adv. Studies Theor. Phys., Vol. 4, (2010), no. 16, 773 - 780
• [7] V. B. L. Chaurasia and S. C. Pandey, it On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions. Astrophys. Space Sci. 317(3) 213-219 (2008)
• [8] G. A. Dorrego and D. Kumar A Generalization of the Kinetic Equation using the Prabhakar - type operators. Honam Mathematical J. 39 (2017), No. 3, pp. 401 416
• [9] B.K. Dutta, L.K. Arora and J. Borah On the Solution of Fractional Kinetic Equation. Gen. Math. Notes, Vol. 6, No. 1, September 2011, pp.40-48 ISSN 2219-7184
• [10] A. Gupta and C. L. Parihar. On solutions of generalized kinetic equations of fractional order. Bol. Soc. Paran. Math., 32(1):181-189, (2014)9 [11] Wagdi F. S. Ahmed, D. D. Pawar Ahmad Y. A. Salamooni On the Solution of Kinetic Equation for Katugampola Type Fractional Differential Equations. Journal of Dynamical Systems and Geometric Theories, 19:1, 125-134
• [12] H.J. Haubold, A.M. Mathai, The fractional kinetic equation and thermonuclear functions. Astrophys. Space Sci. 273 (2000) 53-63.
• [13] R.K. Saxena, S.L. Kalla, On the solutions of certain fractional kinetic equations. Applied Mathematics and Computation 199 (2008) 504-511.
• [14] R. K. Saxena, A. M. Mathai, and H. J. Haubold. Solutions of certain fractional kinetic equations and a fractional diffusion equation. Journal Of Mathematical Physics 51, 103506 (2010)
• [15] M. Mahmoud, Generalized q-Bessel function and its properties. Adv. Difference Equ 1, (2013), 1-11.
• [16] G. M. Mittag-Leffler: Sur la nouvelle function Eα(x). C.R. Acad., Sci.Paris, 137 (1903), 554-558
• [17] F.H. Jackson, The application of basic numbers to Bessel’s and Legendre’s functions, Proc. London Math. Soc. (2) 2 (1904), pp. 192-220.
• [18] M.E.H. Ismail and R. Zhang, q-Bessel functions and Rogers–Ramanujan type identities. (2015). Available at arXiv:1508.06861.
• [19] M. Mansour and M.M. Al-Shomarani, New q-analogy of modified Bessel function and the quantum algebra Eq(2), J. Comput. Anal. Appl. 15(4) (2013), pp. 655-664.
• [20] G. K. Watugala: Sumudu transforms: a new integral transform to solve differential equations and control engineering problems, Int. J. Math. Educ. Sci. Technol., 24 (1993), 35-43