Generalized fractional integration of Bessel function of the first kind

A Study of Saigo-Maeda Fractional Operators With Generalized K-Wright Function

“…During the course of our study, we obtain the images of the generalized K-Wright function in our operators. On account of the most general nature of our results, a large number of results obtained earlier by several authors such as Gehlot and Prajapati [3], Purohit et al [10], Gupta and Gupta [4], Kilbas and Sebestian [7,8,9], Gupta and Gurjar [5], Kilbas [6] follow as special cases of our main findings. …”

Some integrals involving generalized k-Struve functions

“…Properties of this generalized Wright function can be seen in [10,11,9]. In particular, it was proved in [10] that p ψ q (z), z ∈ C is an entire function under the condition (1.5).…”

Certain families of integral formulas involving Struve functions

“…For more detailed properties of p Ψ q including its asymptotic behavior, one may refer to works (for example) [29,30,10,11,12].…”

“…Among those special functions, due mainly to the greater abstruseness of their properties, Bessel functions have found many applications in various problems of mathematical physics (see, e.g., [28]). Recently, a large number of integral formulas involving Bessel functions and their various extensions (or generalizations) have been investigated (see, e.g., [1,4,5,11,12,16,17]). Throughout this paper, let C, R + , N and Z − 0 be the sets of complex numbers, positive real numbers, positive and non-positive integers, respectively, and N 0 := N ∪ {0}.…”