Vol. 11(2). July 2020, No. 22, pp. 270-280.

ON A GENERAL THEOREM CONNECTING LAPLACE TRANSFORM AND GENERALIZED WEYL FRACTIONAL INTEGRAL OPERATOR INVOLVING FOX’S H-FUNCTION AND A GENERAL CLASS OF FUNCTIONS
Vol. 11 (2). July 2020, No. 22, pp. 270-280
VIRENDRA KUMAR

Abstract

The aim of the present paper is to establish a general theorem which asserts an interesting relationship between the Laplace transform and generalized Weyl fractional integral operator involving Fox’s H- function and a general class of functions. The general theorem involves a multidimensional series with essentially arbitrary sequence of complex numbers. By suitably assigning different values to the sequence, one can easily evaluate generalized Weyl fractional integral of special functions of several variables. An illustration for (Srivastava- Daoust) generalized Lauricella function is mentioned. On account of general nature of generalized Lauricella function, Fox’s H-function and general class of functions a number of results involving special functions can be obtained merely by specializing the parameters. For the sake of illustration I have given generalized Weyl fractional integral of elementary special functions including G-function due to Lorenzo-Hartley, which is a generalization of a number of functions of practical utility in fractional calculus.


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