Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the 
generalized (p,q)-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced. 
Further, a new generalized form of the fractional kinetic equation involving the series is also developed. The solutions of 
fractional kinetic equations are presented in terms of the Mittag-Leffler function. The results established here are quite 
general in nature and capable of yielding both known and new results

Fractional Calculus involving (p,q)-Mathieu Type Series

We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

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On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

Generalized fractional kinetic equations involving generalized Struve function of the first kind

The object of the present paper is to derive the solution of generalized kinetic equations of fractional order involving the Wright generalized Bessel function or Bessel–Mitland function. The obtained results in this paper, imply the known results of Chaurasia and Pandey  [24] more precisely in terms of K 4 –function introduced by Sharma [12] believed to be new. Special case, involving the F- function is considered.

On solutions of generalized fractional kinetic equations

In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving Mittag-Leffler function and G-function. This new generalization can be used for the computation of the change of chemical composition in stars like the sun. The manifold generality of the Mittag-Leffler function and G-function is discussed in terms of the solution of the above fractional kinetic equation. Saxena et al. (21, 22) derived the solutions of generalized fractional kinetic equations in terms of Mittaz-Leffler functions by the application of Laplace transform (9, 23). The present work is extension of earlier work done by Saxena et al. (21, 22), and Chaurasia and Pandey (5). 2010 Mathematics Subject Classifications: 44A10, 44A15, 44A35, 44A05, 26A33.

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On the solution of generalized fractional kinetic equations

In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G-function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes contour integral representation of the G-function is also established. The manifold generality of the G-function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R-function, are considered. The obtained results imply more precisely the known results.

On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions

V. B. L. Chaurasia

Papers

On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions