Existence and Uniqueness for the Boundary Value Problems of Nonlinear Fractional Differential Equation

Abstract

This paper studies the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with psi-Caputo fractional derivative

“…So the condition (10) holds with η = 1 2 . We shall check that condition in (11) holds too. for example, α =…”

“…The fractional differential equations (FDEs) have become an emerging area of recent research in science, engineering and mathematics [1][2][3][4]. So, in the literature, there are several studies covering comparable topics to distinct operators such as [1,[5][6][7][8][9][10][11] and the references cited therein. The stability of functional equations was originally raised by Ulam [12] and next by Hyers [13].…”

Some Results on Fractional Differential Equation With Mixed Boundary Condition via S-Iteration

“…Authors are motivated by the above mentioned results and influenced by [1,24]. The main objective of this paper is to extend the some results of the paper [9] by the use of normal S-iteration method which establish the existence and uniqueness of solutions of the boundary value problem (1)-( 2) and other qualitative properties of solutions.…”

"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration"

“…Recently, S. Soltuz and T. Grosan [36] have studied the special version of equation (1.1). Authors are motivated by the work of D. R. Sahu [34] and influenced by [36,37].…”

“…The main objective of this paper is to generalize the results of the paper [37] by the use of normal S−iteration method which establishes the existence and uniqueness of solutions of the boundary value problem (1.1)-(1.2) and other qualitative properties of solutions.…”