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Existence Theory To A Class Of Fractional Order Hybrid Differential Equations

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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)

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.

Suggested Citation

  • Muhammad Naeem Jan & Gul Zaman & Imtiaz Ahmad & Nigar Ali & Kottakkaran Sooppy Nisar & Abdel-Haleem Abdel-Aty & M. Zakarya, 2022. "Existence Theory To A Class Of Fractional Order Hybrid Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-9, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400229
    DOI: 10.1142/S0218348X22400229
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