In this paper, we establish two contour integral representations involving Mittag - Leffler functions (i) for a two variable generalized hypergeometric function of Srivastava and Daoust and (ii) a sum of the Kummer’s confluent hypergeometric functions. Then, we make their appeal to obtain the contour integrals for many generating functions and bilateral generating relations. Further, in development and extensions of fractional calculus, we obtain various relations of contour integrals with fractional derivatives and integral operators to use them in solving of any order initial value problems
In this paper, we introduce certain families of double series associated with general Hurwitz-Lerch type Zeta functions and then derive their summation formulae, series and integral identities. Again then using these identities, we obtain various known and unknown results and hypergeometric generating relations.
In this paper, we exhibit certain double series associated with general hypergeometric type Hurwitz- Lerch Zeta functions and then derive their summation formulae and relations due to their series and integral identities. We also obtain various known and unknown results in terms of Hurwitz-Lerch Zeta functions and their generating relations.
In this paper to define a generalized Churchill’s diffusion problem, we first extend the Churchill’s diffusion problem. Then, we derive some of estimated and computational formulae of its solution. Further, we present a multidimensional Churchill’s diffusion problem consisting of multidimensional Euler space derivatives and Caputo time fractional derivative. Then, on imposing certain boundary values, we obtain its solution and derive its many estimated formulae.
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