A NOVEL COLLECTIVE ALGORITHM USING CUBIC UNIFORM SPLINE AND FINITE DIFFERENCE APPROACHES TO SOLVING FRACTIONAL DIFFUSION SINGULAR WAVE MODEL THROUGH DAMPING-REACTION FORCES

Shao-Wen Yao, Omar Abu Arqub, Soumia Tayebi, M. S. Osman, W. Mahmoud, Mustafa Inc and Hamed Alsulami
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Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, P. R. China
Omar Abu Arqub: ��Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
Soumia Tayebi: ��Department of Mathematics, University of Ahmed Zabana, Relizane, Algeria
M. S. Osman: �Department of Mathematics, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
W. Mahmoud: �Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
Mustafa Inc: ��Department of Medical Research, China Medical University, Taichung, Taiwan, R. O. China
Hamed Alsulami: *Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-13

Abstract: Uses of time-fractional diffusion wave model (TFDWM) in its singular case with damping-reaction terms are widely seen in classical physics applications, e.g. for the quantitative measurement of activity diagnoses light-mechanical waves resulting from many physical experiments. The goal and importance of this paper are to predict and build accurate and convincing numerical solutions for TFDWM in its singular version by employing the collective cubic uniform B-spline approach (CUBSA) and standard finite difference approach (SFDA). The fractional Caputo time derivative (FCTD) has been estimated and broken down using SFDT, whilst the standard splines will be utilized upon realizing spatial discretization. To study the prediction error of our approach, some convergence and bound results are given under certain constraints. We demonstrate applications of our collective algorithm to a couple of fractional singular-type models appearing in fluid dynamics and electromagnetics. Detailed analysis, delegate tables, and representative graphs are displayed and offered in different dimensions to handle the crossover meaning for several order values of FCTDs. Some conclusions, observations, recommendations, and future issues were briefly raised in the final section of this paper.

Keywords: Fractional Caputo Time Derivative; Cubic Uniform Spline Approach; Standard Finite Difference Approach; Diffusion Singular Wave Model (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400698

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