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.
The purpose of this paper is to compute two unified fractional integrals involving the product of two Hfunctions, a general class of polynomials and Appell function F 3 . These integrals are further applied in proving two theorems on Saigo-Maeda fractional integral operators. Some consequent results and special cases are also pointed out in the concluding section.
Fractional kinetic equations (FKEs) including a wide variety of special functions have been widely and successfully applied in describing and solving many important problems of physics and astrophysics. In this paper, we derive the solutions for FKEs including the class of functions with the help of Sumudu transforms. Many important special cases are then revealed and analyzed. The use of the class of functions to obtain the solution of FKEs is fairly general and can be efficiently used to construct several well-known and novel FKEs.
In the present paper, we study and develop the definite integrals of
Gradshteyn-Ryzhik given by Qureshi et al. [3]. The results are in general
character and besides of this have been put in a compact form avoiding the
occurrence of infinite series and thus making them useful in applications.
Several other new and known results can also be obtained from our main
theorems.
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