Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>α</a:mi> </a:math>-Admissible <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>F</c:mi> <c:mfenced open="(" close=")" separators="|"> <c:mrow> <c:msub> <c:mrow> <c:mi>ψ</c:mi> </c:mrow> <c:mrow> <c:mn>1</c:mn> </c:mrow> </c:msub> <c:mo>,</c:mo> <c:msub> <c:mrow> <c:mi>ψ</c:mi> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msub> </c:mrow> </c:mfenced> <c:mo>−</c:mo> </c:math>Contractions in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M3"> <h:mi>M</h:mi> <h:mo>−</h:mo> </h:math>Metric Spaces
Erdal Karapınar, Shimaa I. Moustafa, Ayman Shehata, Ravi P. Agarwal
Abstract
In this paper, we investigate the existence of a unique coupled fixed point for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M4"> <a:mi>α</a:mi> <a:mo>−</a:mo> </a:math> admissible mapping which is of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M5"> <c:mi>F</c:mi> <c:mfenced open="(" close=")" separators="|"> <c:mrow> <c:msub> <c:mrow> <c:mi>ψ</c:mi> </c:mrow> <c:mrow> <c:mn>1</c:mn> </c:mrow> </c:msub> <c:mo>,</c:mo> <c:msub> <c:mrow> <c:mi>ψ</c:mi> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msub> </c:mrow> </c:mfenced> <c:mo>−</c:mo> </c:math> contraction in the context of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M6"> <h:mi>M</h:mi> <h:mo>−</h:mo> </h:math> metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.