Solution approximation of fractional boundary value problems and convergence analysis using AA-iterative scheme

Mujahid Abbas; Cristian Ciobanescu; Muhammad Waseem Asghar; Andrew Omame; Mujahid Abbas; Cristian Ciobanescu; Muhammad Waseem Asghar; Andrew Omame

doi:10.3934/math.2024641

AIMS Mathematics

2024, Volume 9, Issue 5: 13129-13158. doi: 10.3934/math.2024641

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Research article

Solution approximation of fractional boundary value problems and convergence analysis using AA-iterative scheme

1.
Department of Mechanical Engineering Science, Faculty of Engineering and the Built Environment, University of Johannesburg, Johannesburg, South Africa
2.
Department of Medical Research, China Medical University, Taichung 404, Taiwan
3.
Department of Mathematics and Informatics, National University of Science and Technology Politehnica Bucharest, Bucharest 060042, Romania
4.
Department of Mathematics, Government College University Lahore, Lahore 54000, Pakistan
5.
Department of Mathematics, Federal University of Technology, Owerri, Nigeria
6.
Abdus Salam School of Mathematical Sciences, Lahore 54000, Pakistan

Received: 18 January 2024 Revised: 18 March 2024 Accepted: 22 March 2024 Published: 09 April 2024
MSC : 37C25, 47H09, 47H10

Addressing the boundary value problems of fractional-order differential equations hold significant importance due to their applications in various fields. The aim of this paper was to approximate solutions for a class of boundary value problems involving Caputo fractional-order differential equations employing the AA-iterative scheme. Moreover, the stability and data dependence results of the iterative scheme were given for a certain class of mappings. Finally, a numerical experiment was illustrated to support the results presented herein. The results presented in this paper extend and unify some well-known comparable results in the existing literature.
- AA iteration,
- boundary value problems,
- fractional differential equation,
- stability,
- data dependence
Citation: Mujahid Abbas, Cristian Ciobanescu, Muhammad Waseem Asghar, Andrew Omame. Solution approximation of fractional boundary value problems and convergence analysis using AA-iterative scheme[J]. AIMS Mathematics, 2024, 9(5): 13129-13158. doi: 10.3934/math.2024641

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Abstract

Addressing the boundary value problems of fractional-order differential equations hold significant importance due to their applications in various fields. The aim of this paper was to approximate solutions for a class of boundary value problems involving Caputo fractional-order differential equations employing the AA-iterative scheme. Moreover, the stability and data dependence results of the iterative scheme were given for a certain class of mappings. Finally, a numerical experiment was illustrated to support the results presented herein. The results presented in this paper extend and unify some well-known comparable results in the existing literature.

References

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