Application of q-Bessel Functions in the Solution of Generalized Fractional Kinetic Equations
Keywords:Fractional kinetic equations, Laplace transform, fractional integral operator, generalized q-Bessel Functions, Mittag–Leffler functions
AbstractThe present investigation aims to extract a solution from the generalized fractional kinetic equations involving the generalized q-Bessel function by applying the Laplace transform. Methodology and results can be adopted and extended to a variety of related fractional problems in mathematical physics.
G. Agarwal and K. S. Nisar, Certain fractional kinetic equations involving generalized K-functions, Analysis 39(2), (2019), 65–70.
J. Agnihotri.J and G. Agarwal, Solution of fractional kinetic equations by using generalized extended Mittag-Leffler functions, Int. J. Advanced Sc. and Tech. 29(3s), (2020), 1475–1480.
V. B. L. Chaurasia and S. C. Pandey, 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, (2008), 213–219.
V. G. Gupta and B. Sharma, On the solution of generalized fractional kinetic equations, Appl. Math. Sci. 5, (2011), 899–910.
H. J. Haubold and A. M. Mathai, The fractional Kinetic equations and thermonuclear functions, Astrophys. Space Sci. 327, (2000), 53–63.
M. Mahmoud, Generalized q-Bessel function and its properties, Adv. Difference Equ. 1, (2013), 1–11.
K. S. Nisar, S. D. Purohit and S. R. Mondal, Generalized fractional kinetic equations involving generalized Struve function of the first kind, J. King Saud Univ. - Sc., 28, (2016), 167–171.
K. S. Nisar, D. Baleanu and M. Alqurasi, Fractional Calculus and application of generalized Struve functions, Springer Plus, 5, Article No. 910, (2016).
T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J.. 19, (1971), 7–15.
S. G. Samko, A. Kilbas and O. Marichev, Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach, New York (1990).
R. K. Saxena and S. L. Kalla, On the solution of certain fractional kinetic equations, Appl. Math. Comput. 199, (2008), 504–511.