On Stability of Second Order Pantograph Fractional Differential Equations in Weighted Banach Space

Abstract

This work investigates a weighted Banach space second order pantograph fractional differential equation. The considered equation is of second order, expressed in terms of the Caputo–Hadamard fractional operator, and constructed in a general manner to accommodate many specific situations. The asymptotic stability of the main equation’s trivial solution has been given. The primary theorem was demonstrated in a unique manner by employing the Krasnoselskii’s fixed point theorem. We provide a concrete example that supports the theoretical findings.

Keywords

• Caputo–Hadamard fractional derivative
• pantograph fractional differential equations
• Krasnoselskii’s fixed point theorem
• asymptotic stability