Theoretical analysis of a class of φ-Caputo fractional differential equations in Banach space

Abstract

A study of a class of nonlinear differential equations involving the $ \varphi $-Caputo type derivative in a Banach space framework is presented. Weissinger's and Meir-Keeler's fixed-point theorems are used to achieve some quantitative results. Two illustrative examples are provided to justify the theoretical results.

Keywords

• $ \varphi $-caputo derivative
• fixed point theorem
• hausdorff measure of noncompactness