"Theoretical and Computational Aspects of Fractional Hybrid Differentia" by Habibulla Akhadkulov, Ali Fareed Jameel et al.

Progress in Fractional Differentiation & Applications

Article Title

Theoretical and Computational Aspects of Fractional Hybrid Differential Equations

Authors

Habibulla Akhadkulov, School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah Darul Aman, Malaysia\\ Department of General and Exact Sciences, Tashkent State University of Economics, 49 Uzbekistan shoh ko’chasi, Tashkent 100003, Uzbekistan Follow
Ali Fareed Jameel, Faculty of Education and Arts, Sohar University, Sohar 3111, Sultanate of OmanFollow
Teh Yuan Ying, School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah Darul Aman, MalaysiaFollow
Sokhobiddin Akhatkulov, Faculty of Digital Technologies, Samarkand State University, Boulevard st. 15, 140104 Samarkand, UzbekistanFollow
Abdel-Karrem Alomari, Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, 21163, JordanFollow
Dulfikar Jawad Hashim, National University of Science And Technology, Dhi Qar, IraqFollow

Author Country (or Countries)

Uzbekistan

Abstract

This paper is devoted to study the existence and uniqueness of a solution for the following fractional hybrid differential equations defined by Riemann-Liouville differential operator order of 0 < α < 1 http://dx.doi.org/10.18576/pfda/090109 􏰕Dα 􏰍x(t)−f(t,x(t))􏰎=f􏰄t,x(t)􏰅, a.et∈J, t0+ 1 2 (1.0) whereDα istheRiemann-Liouvillefractionalderivativeorderof0<α<1,J=[t ,t +a],forsomet ∈R,a>0, f (·,x)∈Cα(J,R) x(t0) = x0 ∈ R, t0+ α 00 0 1 for all x ∈ R and f2 ∈ L (J × R, R). We prove the existence and uniqueness of a solution of the equation (1.0) by using a coupled fixed point theorem. This result extends the existence theorems of [1,2,3,4]. Moreover, we investigate Picard iterations of an operator T defined on a space of continuous functions under two different weak construction conditions. It is shown that Picard iterations of T converge to the unique fixed point if the weak contraction function is a tangent hyperbolic function. If the weak contraction is a fractional linear function then Picard iterations of T converge to the unique fixed point with an algebraic rate. Finally, we investigate approximate solutions of fractional hybrid differential equations via the homotopy analysis method.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090109

Recommended Citation

Akhadkulov, Habibulla; Fareed Jameel, Ali; Yuan Ying, Teh; Akhatkulov, Sokhobiddin; Alomari, Abdel-Karrem; and Jawad Hashim, Dulfikar (2023) "Theoretical and Computational Aspects of Fractional Hybrid Differential Equations," Progress in Fractional Differentiation & Applications: Vol. 9: Iss. 1, Article 9.
DOI: http://dx.doi.org/10.18576/pfda/090109
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol9/iss1/9

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