EXISTENCE THEORY TO A CLASS OF FRACTIONAL ORDER HYBRID DIFFERENTIAL EQUATIONS

Muhammad Naeem Jan (), Gul Zaman (), Imtiaz Ahmad (), Nigar Ali (), Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty and M. Zakarya
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Muhammad Naeem Jan: Department of Mathematics, University of Malakand, Chakdara, Dir(Lower), Khyber Pakhtunkhwa, Pakistan
Gul Zaman: Department of Mathematics, University of Malakand, Chakdara, Dir(Lower), Khyber Pakhtunkhwa, Pakistan
Imtiaz Ahmad: Department of Mathematics, University of Malakand, Chakdara, Dir(Lower), Khyber Pakhtunkhwa, Pakistan
Nigar Ali: Department of Mathematics, University of Malakand, Chakdara, Dir(Lower), Khyber Pakhtunkhwa, Pakistan
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Abdel-Haleem Abdel-Aty: Department of Physics, College of Sciences, University of Bisha, P. O. Box 344, Bisha 61922, Saudi Arabia4Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
M. Zakarya: Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, 61413 Abha, Saudi Arabia6Department of Mathematics, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-9

Abstract: In this paper, we develop the theory of fractional order hybrid differential equations involving Riemann–Liouville differential operators of order ℓ ∈ (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: Boundary Value Problems; Lipchitz Condition; Lebesgue Dominated Convergence Theorem; Completely Continuous Operator; Fractional Differential Equations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400229

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