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      Fixed Point Theory and the Liouville–Caputo Integro-Differential FBVP with Multiple Nonlinear Terms

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          Abstract

          This work is reserved for the study of a special category of boundary value problems ( BVP s) consisting of Liouville–Caputo integro-differential equations with multiple nonlinear terms. This fractional model and its boundary value conditions (BVCs) involve different simple BVP s, in which the second BVC as a linear combination of two Caputo derivatives of the unknown function equals a nonzero constant. The Banach principle gives a unique solution for this Liouville–Caputo BVP . Further, the Krasnoselskii and Leray–Schauder criteria give the existence property regarding solutions of the mentioned problem. For each theorem, we provide an example based on the required hypotheses and derive numerical data in the framework of tables and figures to show the consistency of results from different points of view.

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          Most cited references37

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          Basic Theory of Fractional Differential Equations

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            Fractional differential equations

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              Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space

              The present paper aims to define three new notions: Θ e -contraction, a Hardy–Rogers-type Θ -contraction, and an interpolative Θ -contraction in the framework of extended b-metric space. Further, some fixed point results via these new notions and the study endeavors toward a feasible solution would be suggested for nonlinear Volterra–Fredholm integral equations of certain types, as well as a solution to a nonlinear fractional differential equation of the Caputo type by using the obtained results. It also considers a numerical example to indicate the effectiveness of this new technique.
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                Author and article information

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                Journal
                Journal of Function Spaces
                Journal of Function Spaces
                Hindawi Limited
                2314-8888
                2314-8896
                February 24 2022
                February 24 2022
                : 2022
                : 1-18
                Affiliations
                [1 ]Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
                [2 ]Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
                [3 ]Laboratory of Applied Mathematics, Kasdi Merbah University, Ouargla B.P. 511 30000, Algeria
                [4 ]Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, Iran
                [5 ]Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
                [6 ]Department of Mathematics and Computer Science, St. Thomas College, Bhilai, Chhattisgarth 49006, India
                Article
                10.1155/2022/6713533
                8522df60-5109-4828-bbcd-4500a7456380
                © 2022

                https://creativecommons.org/licenses/by/4.0/

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