A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative

Abstract

In this article, we address the dual challenges posed by the complexities of fractional calculus and fuzzy uncertainty in mathematical modeling, with a specific focus on the time-fractional heat equation. We introduce a novel concept, the partial generalized Hukuhara conformable fractional derivative, as a bridge between these domains. Complementing this concept, we develop a unique fuzzy tϑϑ-Laplace transform, which enables efficient problem-solving. This transformative approach, coupled with the fuzzy Fourier transform, provides a novel method for deriving fundamental fuzzy solutions for the time-fractional heat equation. We substantiate our approach through successful examples, highlighting its efficacy in complex scenarios. This study pioneers an innovative methodology that unites fractional calculus and fuzzy logic, opening new avenues for addressing real-world challenges.