Caputo-Hadamard fractional boundary-value problems in $ {\mathfrak{L}}^\mathfrak{p} $-spaces

Abstract

The focal point of this investigation is the exploration of solutions for Caputo-Hadamard fractional differential equations with boundary conditions, and it follows the initial formulation of a model that is intended to address practical problems. The research emphasizes resolving the challenges associated with determining precise solutions across diverse scenarios. The application of the Burton-Kirk fixed-point theorem and the Kolmogorov compactness criterion in $ {\mathfrak{L}}^\mathfrak{p} $-spaces ensures the existence of the solution to our problem. Banach's theory is crucial for the establishment of solution uniqueness, and it is complemented by utilizing the Hölder inequality in integral analysis. Stability analyses from the Ulam-Hyers perspective provide key insights into the system's reliability. We have included practical examples, tables, and figures, thereby furnishing a comprehensive and multifaceted examination of the outcomes.

Keywords

• caputo-hadamard fractional derivatives
• ulam-hyers stability
• burton-kirk fixed-point theorem
• hölder inequality
• kolmogorov compactness criterion