Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations-Reference-Cited by-同舟云学术

Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations

Published:2024 Issue:6 Volume:9 Page:15246-15262
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zaky M. A.¹,Babatin M.¹,Hammad M.²,Akgül A.³⁴,Hendy A. S.⁵

Affiliation:

1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

3. Art and Science Faculty, Department of Mathematics, Siirt University, 56100 Siirt, Turkey

4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

5. Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia

Abstract

<abstract><p>Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference26 articles.

1. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equation, Amsterdam: Elsevier, 2006.

2. F. Mainardi, Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models, London: Imperial College Press, 2010.

3. C. J. Li, H. X. Zhang, X. H. Yang, A new nonlinear compact difference scheme for a fourth-order nonlinear Burgers type equation with a weakly singular kernel, J. Appl. Math. Comput., 2024, 1–33. https://doi.org/10.1007/s12190-024-02039-x

4. L. J. Qiao, W. L. Qiu, M. A. Zaky, A. S. Hendy, Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory, Fract. Calc. Appl. Anal., 2024, 1–26. https://doi.org/10.1007/s13540-024-00265-5

5. X. Y. Peng, W. L. Qiu, A. S. Hendy, M. A. Zaky, Temporal second-order fast finite difference/compact difference schemes for time-fractional generalized burgers' equations, J. Sci. Comput., 99 (2024), 52. https://doi.org/10.1007/s10915-024-02514-4