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Topological Degree Theory and Ulam’s Stability Analysis of a Boundary Value Problem of Fractional Differential Equations

In: Frontiers in Functional Equations and Analytic Inequalities

Author

Listed:
  • Amjad Ali

    (Government Postgraduate Jehanzeb College Saidu Sharif Mingora Swat, Department of Mathematics)

  • Kamal Shah

    (University of Malakand, Department of Mathematics)

  • Yongjin Li

    (Sun Yat-sen University, Department of Mathematics)

Abstract

In this article, we study the existence and uniqueness of positive solution to a class of nonlinear fractional order differential equations with boundary conditions. By using fixed point theorems on contraction mapping together with topological degree theory, we investigate some sufficient conditions in order to obtain the existence and uniqueness of positive solution for the considered problem. Further we also investigate different kinds of Ulam stability for the considered problem. Moreover, we also provide an example to justify the whole results.

Suggested Citation

  • Amjad Ali & Kamal Shah & Yongjin Li, 2019. "Topological Degree Theory and Ulam’s Stability Analysis of a Boundary Value Problem of Fractional Differential Equations," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 73-92, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_4
    DOI: 10.1007/978-3-030-28950-8_4
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