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Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem

Author

Listed:
  • Ehsan Pourhadi

    (International Center for Mathematical Modelling in Physics and Cognitive Sciences, Department of Mathematics, Linnaeus University, SE-351 95 Växjö, Sweden
    Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran)

  • Reza Saadati

    (Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
    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)

Abstract

Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

Suggested Citation

  • Ehsan Pourhadi & Reza Saadati & Sotiris K. Ntouyas, 2019. "Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:526-:d:238567
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    References listed on IDEAS

    as
    1. Yumei Zou & Lishan Liu & Yujun Cui, 2014. "The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, March.
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