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The present work looks for the possible existence of static and spherically symmetric wormhole geometries in Rastall-Rainbow gravity. Since, the Rastall-Rainbow gravity model has been constructed with the combination of Rastall theory and the gravity's rainbow formalism. Taking advantage of the Karmarkar condition for embedding class one metrics, we solve the modified field equations analytically that describe wormholes for specific choice of redshift function. For specific parameter ranges, the solution represents a traversable wormhole that exhibits the violation of null energy condition and consequently the weak energy condition also. Furthermore, we focus on the wormhole stability via adiabatic sound velocity analysis. This model establishes a strong connection between two model parameters, namely, the Rastall parameters and the Rainbow functions, and how it affects the wormhole solution., Comment: Accepted for publication in Gen. Relativ. Gravit., 17 pages, 17 figures

In this paper, numerical methods based on Vieta-Lucas wavelets are proposed for solving a class of singular differential equations. The operational matrix of the derivative for Vieta-Lucas wavelets is derived. It is employed to reduce the differential equations into the system of algebraic equations by applying the ideas of the collocation scheme, Tau scheme, and Galerkin scheme respectively. Furthermore, the convergence analysis and error estimates for Vieta-Lucas wavelets are performed. In the numerical section, the comparative analysis is presented among the different versions of the proposed Vieta-Lucas wavelet methods, and the accuracy of the approaches is evaluated by computing the errors and comparing them to the existing findings., Comment: 23 pages, 4 figures, 2 Tables

This research work provides an exhaustive investigation of the viability of different coupled wormhole (WH) geometries with the relativistic matter configurations in the $f(R,G,T)$ extended gravity framework. We consider a specific model in the context of $f(R,G,T)$-gravity for this purpose. Also, we assume a static spherically symmetric space-time geometry and a unique distribution of matter with a set of shape functions ($\beta(r)$) for analyzing different energy conditions (ECs). In addition to this, we examined WH-models in the equilibrium scenario by employing anisotropic fluid. The corresponding results are obtained using numerical methods and then presented using different plots. In this case, $f(R,G,T)$ gravity generates additional curvature quantities, which can be thought of as gravitational objects that maintain irregular WH-situations. Based on our findings, we conclude that in the absence of exotic matter, WH can exist in some specific regions of the parametric space using modified gravity model as, $f(R,G,T) = R +\alpha R^2+\beta G^n+\gamma G\ln(G)+\lambda T$., Comment: Modified, 31 pages, 11 figures

The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin transform and certain generating relations. Also, some important special cases of the main results are pointed out., Comment: 10 pages

The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of Beta function recently defined by Shadab et al.[19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions., Comment: 15

The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with generalized hypergeometric function. To strengthen the main results we also consider many important special cases., Comment: 7 pages

We aim to present two new generalized integral formulae involving product of generalized Struve function $\mathcal{W}_{p,b,c}\left( z\right)$, which are expressed in terms of the generalized Lauricella functions. The main results presented here, being the very general character, reduce to yield known and new integral formulae. Some special cases of our main results are also considered.

We aim to introduce a $\mathtt{k}$-Struve function and investigate its various properties, including mainly certain inequalities associated this function. One of the inequalities given here is pointed out to be related to the so-called classical Tur\'an type inequality. We also present a differential equation, several recurrence relations, and integral representations for this $\mathtt{k}$-Struve function.

In the present research article, we investigate solutions for fractional kinetic equations, involving $\mathtt{k}$-Struve functions, some of the salient properties of which we present. The method used is Laplace transform based. the methodology and results can be adopted and extended to various related fractional problems in mathematical physics.