Solution of Fractional Kinetic Equations Involving generalized q−Bessel function
Year 2022,
, 87 - 95, 31.03.2022
D. D. Pawar
,
Wagdi F. Ahmed
Abstract
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.
References
- [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
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Product of Generalized k-Wright function Bulletin of the Marathwada Mathematical Society
Vol. 20, No.1, June 2019, Pages 22-32
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involving the product of S-function. Mathematical Methods in Engineering. Springer, Cham,
2019. 213-244.
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fractional kinetic equations involving the generalized function for the fractional calculus and
related functions. Astrophys. Space Sci. 317(3) 213-219 (2008)
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- type operators. Honam Mathematical J. 39 (2017), No. 3, pp. 401 416
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Math. Notes, Vol. 6, No. 1, September 2011, pp.40-48 ISSN 2219-7184
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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
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Astrophys. Space Sci. 273 (2000) 53-63.
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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.
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(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
Year 2022,
, 87 - 95, 31.03.2022
D. D. Pawar
,
Wagdi F. Ahmed
References
- [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