On Fractional Differential Equations and Inclusions

Abstract

This thesis investigates the global existence of solutions to fractional diffusion equations involving Caputo fractional derivatives, incorporating nonlinear memory effects and small initial data. We analyze the influence of both the nonlinearity parameter and the fractional derivative order on the admissible range of exponents and the corresponding solution estimates. Our analytical approach combines the Banach fixed-point theorem with established results for the associated linear fractional differential equations.