Fixed-point methodologies and new investments for fuzzy fractional differential equations with approximation results

Abstract

The application of Caputo-Katugampola gH−differentiability to solve systems of fractional partial differential equations is investigated in this work. The existence and uniqueness of two types of gH−weak solutions for fuzzy fractional coupled partial differential equations are established. Lipschitz conditions are employed, and the Banach fixed-point theorem and mathematical induction are used in our approach. To address the challenges of the initial value problems, a matrix-form Cornwall’s inequality is developed. Additionally, a novel analysis of the continuous dependence of the coupled system’s solutions on the given conditions and approximate solutions is provided. An illustrative example is presented to validate the findings.

Keywords

• CK gH-differentiability
• ɛ-approximate solution
• Fuzzy control
• Fixed point technique
• Fractional derivative
• Evaluation metrics