Bilal Basti, Rabah Djemiat, Noureddine Benhamidouche

Theoretical Studies on the Existence and Uniqueness of Solutions for a Multidimensional Nonlinear Time and Space-Fractional Reaction-Diffusion/Wave Equation

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, application of Schauder's and Banach's fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation. The applicability of our main results is demonstrated through examples and explicit solutions.

Mathematics Subject Classification: 35R11, 35A01, 34A08, 35C06, 34K37

Key words and phrases: Multidimensional nonlinear equation, reaction-diffusion/wave, time and space-fractional order, radially symmetric solutions, existence and uniqueness