New insights for the fuzzy fractional partial differential equations pertaining to Katugampola generalized Hukuhara differentiability in the frame of Caputo operator and fixed point technique

Abstract

In this article, we use the Caputo-Katugampola gH-differentiability to solve a class of fractional PDE systems. With the aid of Caputo-Katugampola gH-differentiability, we demonstrate the existence and uniqueness outcomes of two types of gH-weak findings of the framework of fuzzy fractional coupled PDEs using Lipschitz assumptions and employing the Banach fixed point theorem with the mathematical induction technique. Moreover, owing to the entanglement in the initial value problems (IVPs), we establish the p Gronwall inequality of the matrix pattern and inventively explain the continuous dependence of the coupled framework's responses on the given assumptions and the ε-approximate solution of the coupled system. An illustrative example is provided to demonstrate that their existence and unique outcomes are accurate. Through experimentation, we demonstrate the efficacy of the suggested approach in resolving fractional differential equation algorithms under conditions of uncertainty found in engineering and physical phenomena. Additionally, comparisons are drawn for the computed outcomes. Ultimately, we make several suggestions for futuristic work.

Keywords

• Fuzzy set theory
• Caputo-Katugampola fractional derivative operator
• Coupled fractional PDEs
• Continuous dependence and ε-approximation
• Gronwall inequality