Solution of Fractional Differential Equations Utilizing Symmetric Contraction
Aftab Hussain
Abstract
The aim of this paper is to present another family of fractional symmetric <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>α</a:mi> </a:math> - <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>η</c:mi> </c:math> -contractions and build up some new results for such contraction in the context of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mi mathvariant="normal">ℱ</e:mi> </e:math> -metric space. The author derives some results for Suzuki-type contractions and orbitally <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" id="M4"> <h:mi>T</h:mi> </h:math> -complete and orbitally continuous mappings in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" id="M5"> <j:mi mathvariant="normal">ℱ</j:mi> </j:math> -metric spaces. The inspiration of this paper is to observe the solution of fractional-order differential equation with one of the boundary conditions using fixed-point technique in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M6"> <m:mi mathvariant="normal">ℱ</m:mi> </m:math> -metric space.