An Exploration of the Qualitative Analysis of the Generalized Pantograph Equation with the <i>q</i>-Hilfer Fractional Derivative

Abstract

This manuscript tries to show that there is only one solution to the problem of the q-Hilfer fractional generalized pantograph differential equations with a nonlocal condition, and it does so by employing a particular technique known as Schaefer’s fixed point theorem and the Banach contraction principle. Then, we verify that the Ulam-type stability is valid. To illustrate the results, an example is provided.

Keywords

• q-Hilfer fractional derivative
• pantograph equation
• existence
• uniqueness
• Ulam stable
• nonlocal condition