scholarly journals Existence and stability results for nonlinear implicit fractional differential equations with delay and impulses

2016 ◽  
pp. 273-293 ◽  
Author(s):  
Wafaa Albarakati ◽  
Mouffak Benchohra ◽  
Soufyane Bouriah
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Stability Results ◽  
Equations With Delay ◽  
Implicit Fractional Differential Equations

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.

scholarly journals Stability via successive approximation for nonlinear implicit fractional differential equations

2017 ◽  
Vol 3 (1) ◽  
pp. 36-54 ◽  
Author(s):  
Kishor D. Kucche ◽  
Sagar T. Sutar
Keyword(s):  
Differential Equations ◽  
Successive Approximation ◽  
Fractional Differential Equations ◽  
Initial Conditions ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Stability Results ◽  
Implicit Fractional Differential Equations

Abstract In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method.

scholarly journals Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

2015 ◽  
Vol 1 (1) ◽  
pp. 22-37 ◽  
Author(s):  
Mouffak Benchohra ◽  
Soufyane Bouriah
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Fractional Differential ◽  
The Banach Contraction Principle ◽  
Stability Results ◽  
Implicit Fractional Differential Equations

Abstract In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

scholarly journals Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Arshad Ali ◽  
Kamal Shah ◽  
Thabet Abdeljawad ◽  
Ibrahim Mahariq ◽  
Mostafa Rashdan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Proportional Delay ◽  
Integral Boundary ◽  
Impulsive Conditions ◽  
Delay Term ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

AbstractThe current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary conditions. The concerned problem involves proportional type delay term. By using Schaefer’s fixed point theorem and Banach’s contraction principle, the required conditions are developed. Also, different kinds of Ulam stability results are derived by using nonlinear analysis. Providing a pertinent example, we demonstrate our main results.

Sign in / Sign up

Export Citation Format

Share Document