Some results on k-hypergeometric function

In this paper, we establish integral representation and differentiation formulas for k-Gauss hypergeometric function 2F1,k(a, b; c; z) and develops a relationship with k-Confluent hypergeometric function 1F1,k(a, b; c; z), which are based properties defined by Rao and Shukla. Our study is to identify the integral as well differential representation of 2F1,k(a, b; c; z) and also find the inverse Laplace transform on it

Certain expansion formulae involving incomplete I-functions

The aim of this paper is to derive the expansion formulae for the incomplete I-function. Furthermore, their special cases are illustrated in terms of various types of special functions (incomplete I-function, incomplete H-function, and incomplete H-function) that are common in nature and very useful for further analysis.Publisher's Versio

Fractional <i>q</i>-Calculus Operators Pertaining to the <i>q</i>-Analogue of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">M</mi></mrow></semantics></math></inline-formula>-Function and Its Application to Fractional <i>q</i>-Kinetic Equations

In this article, the authors introduce the q-analogue of the M-function, and establish four theorems related to the Riemann–Liouville fractional q-calculus operators pertaining to the newly defined q-analogue of M-functions. In addition, to establish the solution of fractional q-kinetic equations involving the q-analogue of the M-function, we apply the technique of the q-Laplace transform and the q-Sumudu transform and its inverse to obtain the solution in closed form. Due to the general nature of the q-calculus operators and defined functions, a variety of results involving special functions can only be obtained by setting the parameters appropriately

On extended generalized -recurrent (LCS)2n+1-manifolds

We introduce the notion of extended generalized -recurrent (LCS)2n+1-manifolds and study its various geometric properties with example. Finally, we construct an example of 3-dimensional extended generalized -recurrent (LCS)2n+1-manifold which is neither -recurrent nor generalized -recurrent

Integral transforms of the galue type struve function

This paper refers to the study of generalized Struve type function. Using generalized Galu´e type Struve function (GTSF), we derive various integral transforms, including Euler transform, Laplace transform, Whittakar transform, K-transform and fractional Fourier transform. The transform images are expressed in terms of the generalized Wright function. Interesting special cases of the main results are also considered.Publisher's Versio