Study on Krasnoselskii’s fixed point theorem for Caputo–Fabrizio fractional differential equations

Abstract

This note is concerned with establishing existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative. By using usual classical fixed point theorems of Banach and Krasnoselskii, we develop sufficient conditions for the existence of at least one solution and its uniqueness. Further, some results about Ulam-Hyers stability and its generalization are also discussed. Two suitable examples are given to demonstrate the results.

Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

“…Our approach is motivated by the fact that inversion of a perturbed differential operator may result from the sum of a compact operator and a contraction mapping (see [11][12][13] and the references therein). We begin by stating the following Krasnoselskii FPT, which has many applications in studying the existence of solutions to differential equations: Theorem 2.…”

Natural convection flow of a fluid using Atangana and Baleanu fractional model

“…Applying the Laplace transform to Eqs. (8)- (12) and utilizing the definition given in Eq. 14, we get…”

“…Jarad et al [10] developed a new class of fractional operators in the Reimann-Liouville and Caputo sense. Some relevant references to the fractional integrals and their applications can be found in [11][12][13][14][15] and the references therein.…”

Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem

“…Therefore, different types of fixed point results have proved its usefulness for the research work in the field of arbitrary-order differential equations. For instance, [18] is devoted to the existence of solutions for implicit differential equations including Caputo-Fabrizio operators through the application of Banach and Krasnosel'skii fixed point results, analyzing also some stability properties. An analogous study for equations with Caputo-Hadamard derivative is made in [19].…”