Abstract
The generalized fractional integrations of the generalized Mittag-Leffler type function (GMLTF) are established in this paper. The results derived in this paper generalize many results available in the literature and are capable of generating several applications in the theory of special functions. The solutions of a generalized fractional kinetic equation using the Sumudu transform is also derived and studied as an application of the GMLTF.
Highlights
INTRODUCTIONThe Pochhammer symbol (̟ )n is defined by (for ∈ C)[see ([1], p. 2 and p. 5)]:. (̟ ∈ C \ Z−0 )
The Pochhammer symbol (̟ )n is defined by[see ([1], p. 2 and p. 5)]: (n = 0)(̟ )n : = ̟ (̟ + 1) . . . (̟ + n − 1) (n ∈ N) (1) = Ŵ(̟ + n) Ŵ(̟ ) (̟ ∈ C \ Z−0 ).The familiar generalized hypergeometric function pFq is defined as follows: pFqp χq ; ; x ∞ = n=0 p j=1 q j=1
We studied the generalized fractional calculus of more generalized function given in (7)
Summary
The Pochhammer symbol (̟ )n is defined by (for ∈ C)[see ([1], p. 2 and p. 5)]:. (̟ ∈ C \ Z−0 ). The familiar generalized hypergeometric function pFq is defined as follows (see [2]): pFqp χq. If p = 2 and q = 1, (2) reduces to the Gaussian hypergeometric function. The function r s(z) is the generalized Wright hypergeometric series which is given by r s(z) = r s (ai, ̟i)1,r (bj, χj)1,s z k=0 r i=. Many more generalizations and extensions of MLF widely studied recently [9, 10]. Nisar [14] defined a generalized Mittag-Leffler type function which is defined as follows. For more details one can be referred to Nisar [14]
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