Generalized fractional operator representations of Jacobi type orthogonal polynomials

The aim of this paper is to apply generalized operators of fractional integration and differentiation involving Appell's function $F_{3}(:)$ due to Marichev-Saigo-Maeda (MSM), to the Jacobi type orthogonal polynomials. The results are expressed in terms of generalized hypergeometric function. Some of the interesting special cases of the main results also established

Marichev-Saigo-Maeda fractional operator representations of generalized Struve function

The aim of this paper is to apply generalized operators of fractional integration and differentiation involving Appells function due to Marichev-Saigo-Maeda, to the generalized Struve function. The results are expressed in terms of generalized Wright function. The results obtained here are general in nature and can easily obtain various known results

Some unified integrals associated with Bessel-Struve kernel function

In this paper, we discuss the generalized integral formula involving Bessel-Struve kernel function $S_{\alpha }\left( \lambda z\right)$, which expressed in terms of generalized Wright functions. Many interesting special cases also obtained in this study.Comment: 8 page

Marichev-Saigo-Maeda fractional integration operators of generalized Bessel functions

Two integral operator involving the Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind are expressed in term of generalized Wright function and generalized hypergeometric series. Many special cases, including cosine and sine function are also discussed.Comment: 13 page

Unified integral operator involving generalized Bessel-Maitland function

The main object of this article is to present an interesting double integral involving generalized Bessel-Maitland function defined by Ghaysuddin et al., which is expressed in terms of generalized (Wright) hypergeometric function. We also considered some special cases as an application of the main result

Composition formulas of Bessel-Struve kernel function

The generalized operators of fractional integration involving Appell's function $F_{3}(.)$ due to Marichev-Saigo-Maeda, is applied to the Bessel Struve kernel function $S_{\alpha }\left( \lambda z\right),\lambda ,z\in \mathbb{C}$ to obtain the results in terms of generalized Wright functions.The pathway integral representations Bessel Struve kernel function and its relation between many other functions also derived in this study.Comment: 13 page

A New Class of Integrals Involving Extended Hypergeometric Function

Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain special cases of the main results presented here are also pointed out for the extended Gauss' hypergeometric and confluent hypergeometric functions

(p,q)(p,q)-Whittaker function and associated properties and formulas

Recently, various extensions and variants of Bessel functions of several kinds have been presented. Among them, the $(p,q)$-confluent hypergeometric function $\Phi_{p,q}$ has been introduced and investigated. Here, we aim to introduce an extended $(p,q)$-Whittaker function by using the function $\Phi_{p,q}$ and establish its various properties and associated formulas such as integral representations, some transformation formulas and differential formulas. Relevant connections of the results presented here With those involving relatively simple Whittaker functions are also pointed out

Some Unified Integrals Associated with Generalized Bessel-Maitland Function

Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results, we obtained some interesting results of ordinary Bessel function

Inequalities of extended (p,q)-beta and confluent hypergeometric function

In this present paper, we establish the log-convexity and Tur\'an type inequalities of extended $(p,q)$-beta functions. Also, we present the log-convexity, the monotonicity and Tur\'an type inequalities for extended $(p,q)$-confluent hypergeometric function by using the inequalities of extended $(p,q)$-beta functions.Comment: 9 page