Fixed-Point Analysis, Stability, and Computational Well-Posedness of a Fractional Stochastic Magnetoconvection Model in a Porous Vertical Annulus
Category : ERJ: VOLUME 1, Issue 10 (October 2021)
Fixed-Point Analysis, Stability, and Computational Well-Posedness of a Fractional Stochastic Magnetoconvection Model in a Porous Vertical Annulus
1*MKPEDEM K. A; 2OLAYIWOLA R.O; 3FADEPO J. T.
1. *Department of Mathematics, University of Abuja, Nigeria.
2. Department of Industrial Mathematics, Federal University of Science and Technology, Minna, Niger State, Nigeria.
3. Department of Industrial Mathematics, Federal University of Science and Technology, Minna, Niger State, Nigeria.
Corresponding author: *kufremkpedem@gmail.com, olayiwola.rasaq@Futminna.edu.ng, fadepoj@gmail.com
Abstract
This study investigates a fractional stochastic magnetoconvection model describing the natural convection flow of an electrically conducting fluid in a porous vertical annulus with variable thermal conductivity. The governing momentum and energy equations are formulated using the Caputo–Fabrizio fractional derivative to incorporate memory effects, while stochastic perturbations are introduced to account for random environmental and thermal fluctuations. Rather than seeking analytical solutions, the study focuses on establishing the mathematical validity and computational admissibility of the proposed model. The governing system is reformulated as an equivalent system of fractional integral equations, and an associated solution operator is constructed within an appropriate Banach space. The boundedness and Lipschitz continuity of the nonlinear operators are established, and fixed-point theory is employed to investigate the existence and uniqueness of solutions. Using the Banach Fixed Point Theorem, sufficient conditions guaranteeing a unique solution are obtained. The results further demonstrate that the model is well-posed and suitable for reliable numerical computation and future simulation studies.
Keywords: Fractional calculus, Caputo–Fabrizio derivative, fixed-point theorem, stochastic magnetoconvection, porous vertical annulus, existence and uniqueness, well-posedness.
