Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part IIOpen Access

EXISTENCE THEORY TO A CLASS OF FRACTIONAL ORDER HYBRID DIFFERENTIAL EQUATIONS

MUHAMMAD NAEEM JAN

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

E-mail Address: naeemjan2345@uom.edu.pk

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GUL ZAMAN

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

E-mail Address: gzaman@uom.edu.pk

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IMTIAZ AHMAD

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

E-mail Address: iahmad@uom.edu.pk

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NIGAR ALI

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

E-mail Address: nigaruom@gmail.com

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KOTTAKKARAN SOOPPY NISAR

Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

E-mail Address: n.sooppy@psau.edu.sa

E-mail Address: ksnisar1@gmail.com

Corresponding author.

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ABDEL-HALEEM ABDEL-ATY

Department of Physics, College of Sciences, University of Bisha, P. O. Box 344, Bisha 61922, Saudi Arabia

Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

E-mail Address: halimaty@gmail.com

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, and

M. ZAKARYA

Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, 61413 Abha, Saudi Arabia

Department of Mathematics, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt

E-mail Address: Mohammed_Zakaria1983@yahoo.com

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https://doi.org/10.1142/S0218348X22400229Cited by:6 (Source: Crossref)

Abstract

In this paper, we develop the theory of fractional order hybrid differential equations involving Riemann–Liouville differential operators of order $ℓ \in (0, 1)$ . We study the existence theory to a class of boundary value problems for fractional order hybrid differential equations. The sum of three operators is used to prove the key results for a couple of hybrid fixed point theorems. We obtain sufficient conditions for the existence and uniqueness of positive solutions. Moreover, examples are also presented to show the significance of the results.

Keywords:

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Vol. 30, No. 01

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History

Received 20 February 2021

Accepted 31 May 2021

Published: September 3, 2021

Information

This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part II”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Khan Muhammad (Sejong University, South Korea), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) 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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EXISTENCE THEORY TO A CLASS OF FRACTIONAL ORDER HYBRID DIFFERENTIAL EQUATIONS

Abstract

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