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Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations

Author

Listed:
  • Hanadi Zahed

    (Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara 41411, Saudi Arabia)

  • Hoda A. Fouad

    (Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara 41411, Saudi Arabia
    Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21500, Egypt)

  • Snezhana Hristova

    (Department of Applied Mathematics and Modeling, University of Plovdiv “Paisii Hilendarski”, 4000 Plovdiv, Bulgaria)

  • Jamshaid Ahmad

    (Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2).

Suggested Citation

  • Hanadi Zahed & Hoda A. Fouad & Snezhana Hristova & Jamshaid Ahmad, 2020. "Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 8(7), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1168-:d:385219
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