On Finite-Time Blow-Up Problem for Nonlinear Fractional Reaction Diffusion Equation: Analytical Results and Numerical Simulations-Reference-Cited by-同舟云学术

On Finite-Time Blow-Up Problem for Nonlinear Fractional Reaction Diffusion Equation: Analytical Results and Numerical Simulations

Published:2023-07-30 Issue:8 Volume:7 Page:589
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Hamadneh Tareq¹,Chebana Zainouba²^ORCID,Abu Falahah Ibraheem³,AL-Khassawneh Yazan Alaya⁴^ORCID,Al-Husban Abdallah⁵,Oussaeif Taki-Eddine²,Ouannas Adel²,Abbes Abderrahmane⁶⁷^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11733, Jordan

2. Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria

3. Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13133, Jordan

4. Data Science and Artificial Intelligence Department, Zarqa University, Zarqa 13133, Jordan

5. Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan

6. Department of Mathematics, Badji Mokhtar-Annaba University, Annaba 23000, Algeria

7. Laboratory of Mathematics, Dynamics and Modelization, Badji Mokhtar-Annaba University, Annaba 23000, Algeria

Abstract

The study of the blow-up phenomenon for fractional reaction–diffusion problems is generally deemed of great importance in dealing with several situations that impact our daily lives, and it is applied in many areas such as finance and economics. In this article, we expand on some previous blow-up results for the explicit values and numerical simulation of finite-time blow-up solutions for a semilinear fractional partial differential problem involving a positive power of the solution. We show the behavior solution of the fractional problem, and the numerical solution of the finite-time blow-up solution is also considered. Finally, some illustrative examples and comparisons with the classical problem with integer order are presented, and the validity of the results is demonstrated.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/8/589/pdf

Reference28 articles.

1. Some problems of the theory of differential equations;Samarskii;Differ. Uravn.,1980

2. Coddigton, E.A., and Levinson, N. (1955). Theory of Ordinary Differential Equations, McGraw–Hill.

3. Cartan, H. (1967). Cours de Calcul Différentiel, Hermann Paris, Collection Méthodes, Editeurs des Sciences et Arts.

4. The solution of the heat equation anubject to the specification of energy;Cannon;Q. Appl. Math.,1963

5. Demailly, J.P. (2006). Analyse numérique et équations diff érentielles, in Presses Universitaires de Grenoble . EDP Sci., 237–243.