Existence and analysis of Hilfer-Hadamard fractional differential equations in RLC circuit models

Abstract

This paper explores a fractional integro-differential equation with boundary conditions that incorporate the Hilfer-Hadamard fractional derivative. We model the RLC circuit using fractional calculus and define weighted spaces of continuous functions. The existence and uniqueness of solutions are established, along with their Ulam-Hyers and Ulam-Hyers-Rassias stability. Our analysis employs Schaefer's fixed-point theorem and Banach's contraction principle. An illustrative example is presented to validate our findings.

Keywords

• fractional differential equations
• hilfer-hadamard fractional derivative
• non-local boundary conditions
• existence
• fixed-point theorem