An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

Our aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize th...

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Veröffentlicht in:Advances in difference equations Jg. 2021; H. 1; S. 1 - 18
Hauptverfasser: Al-Smadi, Mohammed, Djeddi, Nadir, Momani, Shaher, Al-Omari, Shrideh, Araci, Serkan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 26.05.2021
Springer Nature B.V
SpringerOpen
Schlagworte:
Abel-type differential equation
Algorithms
Analysis
Caputo–Fabrizio fractional derivative
Convergence
Difference and Functional Equations
Differential equations
Error analysis
Exact solutions
Functional Analysis
Hilbert space
Kernels
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical solution
Ordinary Differential Equations
Partial Differential Equations
Reproducing kernel algorithm
Abel-type differential equation
Caputo–Fabrizio fractional derivative
Error analysis
Reproducing kernel algorithm
Numerical solution
ISSN:1687-1847, 1687-1839, 1687-1847
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Zusammenfassung:Our aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize the Gram–Schmidt orthogonalization process to create an orthonormal set of bases that leads to an appropriate solution in the Hilbert space H 2 [ a , b ] . We investigate and discuss stability and convergence of the proposed method. The n -term series solution converges uniformly to the analytic solution. We present several numerical examples of potential interests to illustrate the reliability, efficacy, and performance of the method under the influence of the Caputo–Fabrizio derivative. The gained results have shown superiority of the reproducing kernel algorithm and its infinite accuracy with a least time and efforts in solving the fractional Abel-type model. Therefore, in this direction, the proposed algorithm is an alternative and systematic tool for analyzing the behavior of many nonlinear temporal fractional differential equations emerging in the fields of engineering, physics, and sciences.
Bibliographie:ObjectType-Article-1
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03428-3