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A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique

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  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    These authors contributed equally to this work.)

  • Chernet Tuge Deressa

    (Department of Mathematics, College of Natural Sciences, Jimma University, Jimma, Ethiopia
    These authors contributed equally to this work.)

  • Azhar Hussain

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
    These authors contributed equally to this work.)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 751-71379, Iran
    These authors contributed equally to this work.)

  • Reny George

    (Department of Mathematics, College of Science and Humanities in AlKharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics and Computer Science, St. Thomas College, Bhilai 490006, India
    These authors contributed equally to this work.)

  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

Few studies have investigated the existence and uniqueness of solutions for fractional differential equations on star graphs until now. The published papers on the topic are based on the assumption of existence of one junction node and some boundary nodes as the origin on a star graph. These structures are special cases and do not cover more general non-star graph structures. In this paper, we state a labeling method for graph vertices, and then we prove the existence results for solutions to a new family of fractional boundary value problems (FBVPs) on the methylpropane graph. We design the chemical compound of the methylpropane graph with vertices specified by 0 or 1, and on every edge of the graph, we consider fractional differential equations. We prove the existence of solutions for the proposed FBVPs by means of the Krasnoselskii’s and Scheafer’s fixed point theorems, and further, we study the Ulam–Hyers type stability for the given multi-dimensional system. Finally, we provide an illustrative example to examine our results.

Suggested Citation

  • Shahram Rezapour & Chernet Tuge Deressa & Azhar Hussain & Sina Etemad & Reny George & Bashir Ahmad, 2022. "A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:568-:d:747688
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    References listed on IDEAS

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    1. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Mohammed M. Matar & Esmail S. Abu Skhail, 2018. "On Stability of Nonautonomous Perturbed Semilinear Fractional Differential Systems of Order," Journal of Mathematics, Hindawi, vol. 2018, pages 1-10, August.
    3. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad, 2019. "Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
    4. Badr Alqahtani & Hassen Aydi & Erdal Karapınar & Vladimir Rakočević, 2019. "A Solution for Volterra Fractional Integral Equations by Hybrid Contractions," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
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