Existence and Stability of Hybrid Hyperbolic Partial Inclusions and Equations Within A $\psi$--Caputo Fractional Derivative in Banach Algebra

Abstract

This study examines two new hyperbolic partial differential equations. One is a hybrid hyperbolic fractional differential inclusion, while the other is a hybrid hyperbolic fractional differential equation including a collective fractional derivative referred to as the ψ–Caputo fractional operator. The Dhage fixed point theorem is utilized to demonstrate the existence of solutions for the aforementioned equations, while their uniqueness is addressed using the Banach fixed point theorem. Additionally, the stability of solutions to these equations within the framework of Ulam–Hyers is also examined. Two relevant examples are provided to substantiate the provided findings.

Keywords

• \psi fractional operaator
• Inclusions
• Hyperbolic partial differential equations

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