ArticleOpen Access

USING A PRIOR ESTIMATE METHOD TO INVESTIGATE SEQUENTIAL HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS

GHAZALA NAZIR

Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan

E-mail Address: ghazalanazir732@gmail.com

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KAMAL SHAH

Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan

E-mail Address: kamalshah408@gmail.com

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THABET ABDELJAWAD

Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia

Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Department of Computer Science and Information Engineering Asia University, Taichung, Taiwan

E-mail Address: tabdeljawad@psu.edu.sa

Corresponding author.

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HAMMAD KHALIL

Department of Mathematics, University of Education Attock Campus Punjab, Pakistan

E-mail Address: hammadk310@gmail.com

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, and

RAHMAT ALI KHAN

Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan

E-mail Address: rahmat_alipk@yahoo.com

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https://doi.org/10.1142/S0218348X20400046Cited by:7 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this paper, our main objective is to develop the conditions that assure the existence of solution to a system of boundary value problems (BVPs) of sequential hybrid fractional differential equations (SHFDEs). The problem is considered under the nonlinear boundary conditions. Nonlinear functions involved in the considered system of SHFDEs are continuous and satisfy the growth conditions. We convert the system of SHFDEs to the system of fixed points problem by using the technique of the topological degree theory also called prior estimate method. We establish sufficient conditions that guarantee the existence and uniqueness of positive solution to the system under consideration. Moreover, suitable results are also developed for the Hyers–Ulam stability analysis for the solution of the considered problem. An example is also included to reveal our main result.

Keywords:

References

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Vol. 28, No. 08

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History

Received 17 December 2019

Accepted 3 March 2020

Published: July 10, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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USING A PRIOR ESTIMATE METHOD TO INVESTIGATE SEQUENTIAL HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

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