Utilizing Schaefer's fixed point theorem in nonlinear Caputo sequential fractional differential equation systems

Abstract

In the present study, established fixed-point theories are utilized to explore the requisite conditions for the existence and uniqueness of solutions within the realm of sequential fractional differential equations, incorporating both Caputo fractional operators and nonlocal boundary conditions. Subsequently, the stability of these solutions is assessed through the Ulam-Hyers stability method. The research findings are validated with a practical example that corroborate and reinforce the theoretical results.

Keywords

• caputo fractional derivative
• existence and uniqueness
• sequential derivatives
• fixed point theorem
• boundary conditions