Existence and Stability Results for Fractional Differential Equations With Two Caputo Fractional Derivatives

Abstract

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

Solvability and Mittag–Leffler–Ulam stability for fractional Duffing problem with three sequential fractional derivatives

“…In differential equations, the fractional derivative operators have shown its wings in the modeling of several problems in science, engineering, and technology as can be seen in earlier studies [1][2][3][4][5][6][7][8][9] and the references therein. In quite recent times, many researchers have given the existence, uniqueness, and various structures of Ulam stability and Mittag-Leffler-Ulam stability of solutions for differential equations of fractional order as in previous research [10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein.…”

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“…Different fixed point theorems such as the Banach contraction principle, Schaefer’s fixed point theorem, Krasnoselskii’s fixed point theorem, and the Leray-Schauder nonlinear alternative lead to some exciting results on the existence and uniqueness of solutions of differential equations (DEs) [ 15 ]. The stability of solutions of DEs has drawn attention from mathematicians, physicists, and computer scientists.…”

Nonlinear two conformable fractional differential equation with integral boundary condition

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