Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

Abstract

This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

Comparative analysis of oldroyd-b and casson nanofluids flowing through chemically reactive radiative porous medium

“…The converted problem is then tackled through the famous analytical scheme named homotopy analysis method (HAM). [27][28][29][30][31][32] The convergent of the computed results is verified through plots and numeric benchmark. The results of distinct physical quantities are elaborated through graphs.…”

On Ψ-Hilfer Fractional Integro-Differential Equations with Non-Instantaneous Impulsive Conditions

“…The reason for this is FDEs accurately describe many real-world phenomena such as biology, physics, chemistry, signal processing, and many more (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13]). Furthermore, it should be remarked that FDEs have interesting applications in solving inverse problems, and in the modeling of heat flow in porous material (see, e.g., [14][15][16][17][18][19][20][21][22][23][24][25]).…”

On Nonlinear Ψ-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions

“…The reason for this is FDEs efficiently describe many real-world processes such as in chemistry, biology, signal processing, and many others (see, e.g., [4,[7][8][9]13,[17][18][19][20][21]). Additionally, FDEs have interesting applications in solving inverse problems, and in the modeling of heat flow in porous material (see, e.g., [22][23][24]).…”