Space-Dependent Fractional Evolution Equations: A New Approach

2025/02/18 by Tiago Augusto dos Santos Boza, Boza, Tiago Augusto dos Santos, Paulo Mendes de Carvalho Neto +1
Mathematics · #26A33 #35A01 #35A02 #35Q92 #35R11 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2502.12730

openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the works of \citebaz2 and \citekian, 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.

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