Generalized Caputo-Katugampola for solving fuzzy fractional Heat Equation.

This paper explores the application of fuzzy theory to solve fractional heat equations using a novel approach, the Optimal Homotopy Asymptotic Method (OHAM). We introduce a semi-analytical method to address fuzzy fractional-order heat equations, aiming to overcome the limitations of existing approaches. Our methodology leverages the generalized Caputo-Katugampola (CK) definition with two parameters α and ρ, to define fractional derivatives. Through this research, we present a comprehensive framework for tackling this challenging problem. To illustrate the effectiveness and feasibility of our method, we provide several practical examples. The results are presented in tables and figures, and our approach is compared to the exact solutions. This study not only contributes to the field but also offers a powerful and efficient way to address fuzzy fractional heat equations with increased accuracy and reduced computational effort. [ABSTRACT FROM AUTHOR]