[Generalized Telegraph equation with fractional $p(x)$-Laplacian

TL;DR

This paper investigates the existence of solutions for a generalized fractional telegraph equation involving a variable exponent p(x)-Laplacian and extcolor{red}{ ext{psi}}-Hilfer fractional derivatives, expanding the mathematical understanding of such complex differential equations.

Contribution

It introduces a new framework for analyzing generalized fractional telegraph equations with extcolor{red}{ ext{psi}}-Hilfer derivatives and variable exponent p(x)-Laplacian, addressing existence of solutions.

Findings

Existence of solutions established under certain conditions.

Extended the theory of fractional telegraph equations.

Provided new methods for fractional differential equations with variable exponents.

Abstract

The purpose of this paper is devoted to \textcolor{red}{discussing} the existence of solutions for a generalized fractional telegraph equation involving a class of $\psi$-Hilfer fractional with $p(x)$-Laplacian differential equation.