Fixed point approach to solve fractional differential equations in $ S^{JS} $-metric spaces

Doaa Rizk; Nizar Souayah; Nabil Mlaiki; Doaa Rizk; Nizar Souayah; Nabil Mlaiki

doi:10.3934/math.2022858

AIMS Mathematics

2022, Volume 7, Issue 8: 15680-15692. doi: 10.3934/math.2022858

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Research article

Fixed point approach to solve fractional differential equations in $ S^{JS} $-metric spaces

1.
Department of Mathematics, College of Science and Arts, Qassim University, Saudi Arabia
2.
Department of Natural Sciences, Community College Al-Riyadh, King Saud University
3.
Ecole Supérieure des Sciences Economiques et Commerciales de Tunis, Université de Tunis, Tunisia
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia 11586

Received: 03 May 2022 Revised: 18 June 2022 Accepted: 21 June 2022 Published: 24 June 2022
MSC : 47H10, 54H25

This study aims to establish a new fixed point theorem in the framework of $ S^{JS} $-metric spaces, recently introduced by Beg et al. We propose different principles of contraction using various techniques. The theorems obtained represent a new framework for other future work in the considered space. Also, we provide two applications of our results to linear system of equations and the following fractional differential equation

$ \mathcal{(P)}:\left\{ \begin{array}{ccl} D^{\lambda}x(t) & = & f(t, x(t)) = Fx(t) \mbox{ if } t\in I_0 = (0, T] \\ x(0) & = & x(T) = r \ \end{array} \right\}. $

These applications show the effectiveness of our approach as a powerful tool for solving several types of differential equations.
- fixed point,
- $ S^{JS} $-metric spaces,
- system of linear equations,
- fractional differential equations
Citation: Doaa Rizk, Nizar Souayah, Nabil Mlaiki. Fixed point approach to solve fractional differential equations in $ S^{JS} $-metric spaces[J]. AIMS Mathematics, 2022, 7(8): 15680-15692. doi: 10.3934/math.2022858

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Abstract

This study aims to establish a new fixed point theorem in the framework of $ S^{JS} $-metric spaces, recently introduced by Beg et al. We propose different principles of contraction using various techniques. The theorems obtained represent a new framework for other future work in the considered space. Also, we provide two applications of our results to linear system of equations and the following fractional differential equation

$ \mathcal{(P)}:\left\{ \begin{array}{ccl} D^{\lambda}x(t) & = & f(t, x(t)) = Fx(t) \mbox{ if } t\in I_0 = (0, T] \\ x(0) & = & x(T) = r \ \end{array} \right\}. $

These applications show the effectiveness of our approach as a powerful tool for solving several types of differential equations.

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