A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel–Wright Function

Abstract

In this paper, the operators of fractional integration introduced by Marichev-Saigo-Maeda involving Appell's function F 3 (•) are applied, and several new image formulas of generalized Lommel-Wright function are established. Also, by implementing some integral transforms on the resulting formulas, few more image formulas have been presented. We can conclude that all derived results in our work generalize numerous well-known results and are capable of yielding a number of applications in the theory of special functions.

Commentary: A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel-Wright Function

“…Then, it is a turn to consider the nature of the generalized Lommel-Wright function treated in the commented paper [1]. There, we find its definition (1.1) and also a representation as a generalized Wright hypergeometric function (1.2), namely:…”

“…The commented paper [1] is one example of a long list of recently published works devoted to evaluation of the images of classes of special functions under the classical operators of fractional order integration and differentiation and their various generalizations. The used procedures are usually same standard ones [interchanging the order of integration and summation, as in (2.3), [1]]. And in many cases the resulting expressions are complicated and involve special functions different in kind from the originals.…”

“…First, let us comment on the so-called Marichev-Saigo-Maeda (MSM) operator of FC (for shortness of place we consider only the left-hand sided I 0+ version), as it is defined by (1.10) in Agarwal et al [1], and also after a substitution σ = t/x, as:…”

“…various such representations of (7) are provided, as the mentioned symmetry allows this. Here, for the purpose to compare with the results in Agarwal et al [1], we mention the following representation in terms of (4) and (3):…”

Application of fractional differential equations to heat transfer in hybrid nanofluid: modeling and solution via integral transforms

“…Jain ([17], p. 1-11) introduced a novel and powerful numerical scheme and implemented to different fractional order differential equations. Some other interesting and significant studies on fractional derivatives can be found in [18][19][20][21][22][23][24][25][26] and the references therein.…”