A solution of a fractional differential equation via novel fixed-point approaches in Banach spaces

Junaid Ahmad; Kifayat Ullah; Hasanen A. Hammad; Reny George; Junaid Ahmad; Kifayat Ullah; Hasanen A. Hammad; Reny George

doi:10.3934/math.2023636

AIMS Mathematics

2023, Volume 8, Issue 6: 12657-12670. doi: 10.3934/math.2023636

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Research article

A solution of a fractional differential equation via novel fixed-point approaches in Banach spaces

1.
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan
2.
Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
3.
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
5.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Received: 11 December 2022 Revised: 08 March 2023 Accepted: 14 March 2023 Published: 29 March 2023
MSC : 47H09, 47H10

This manuscript is devoted to presenting some convergence results of a three-step iterative scheme under the Chatterjea–Suzuki–C ((CSC), for short) condition in the setting of a Banach space. Also, an example of mappings satisfying the (CSC) condition with a unique fixed point is provided. This example proves that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Finally, our main results will be applied to find a solution to functional and fractional differential equations (FDEs) as an application.
- three-step iteration,
- differential equation,
- $ (CSC) $ condition,
- weak and strong convergence,
- Banach space
Citation: Junaid Ahmad, Kifayat Ullah, Hasanen A. Hammad, Reny George. A solution of a fractional differential equation via novel fixed-point approaches in Banach spaces[J]. AIMS Mathematics, 2023, 8(6): 12657-12670. doi: 10.3934/math.2023636

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Abstract

This manuscript is devoted to presenting some convergence results of a three-step iterative scheme under the Chatterjea–Suzuki–C ((CSC), for short) condition in the setting of a Banach space. Also, an example of mappings satisfying the (CSC) condition with a unique fixed point is provided. This example proves that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Finally, our main results will be applied to find a solution to functional and fractional differential equations (FDEs) as an application.

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