Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations

Hanadi Zahed, Hoda A. Fouad, Snezhana Hristova and Jamshaid Ahmad
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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
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

Mathematics, 2020, vol. 8, issue 7, 1-19

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).

Keywords: fixed point; complete metric space; fractional differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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