Space-Dependent Fractional Evolution Equations: A New Approach

TL;DR

This paper introduces a new abstract framework for analyzing differential equations with space-dependent fractional derivatives, establishing foundational results on existence and uniqueness, and exploring their mathematical properties and applications.

Contribution

It develops a novel approach for space-dependent fractional evolution equations, extending existing theories to include spatial variability in fractional derivatives.

Findings

Established existence and uniqueness of solutions.

Provided insights into the influence of spatially varying fractional derivatives.

Enhanced understanding of mathematical properties and potential applications.

Abstract

Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish existence and uniqueness results for solutions in both linear and semilinear settings. Our findings provide deeper insights into how spatially varying fractional derivatives influence the behavior of differential equations, shedding light on their mathematical properties and potential applications.