Existence and Stability of Nonlinear Implicit Caputo-Exponential Fractional Differential Equations

2022 ◽  
Vol 8 (1) ◽  
pp. 91-105
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Stability ◽  
Fractional Differential

scholarly journals EXISTENCE AND STABILITY RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO FRACTIONAL DERIVATIVES

2019 ◽  
pp. 341
Author(s):  
Mohamed Houas ◽  
Mohamed Bezziou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Contraction Mapping ◽  
Nonlocal Boundary ◽  
Stability Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Stability Results

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.

On the behavior of solutions of fractional differential equations on time scale via Hilfer fractional derivatives

2018 ◽  
Vol 21 (4) ◽  
pp. 1120-1138 ◽  
Author(s):  
Devaraj Vivek ◽  
Kuppusamy Kanagarajan ◽  
Seenith Sivasundaram
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.

scholarly journals Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

2018 ◽  
Vol 17 (1) ◽  
pp. 103-125 ◽  
Author(s):  
Akbar Zada ◽  
Mohammad Yar ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Caputo Fractional Differential Equations ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document