Existence and stability of solutions of a class of hybrid fractional differential equations involving RL-operator

2020 ◽  
Vol 23 (4) ◽  
pp. 885-903 ◽  
Author(s):  
Soumia Ferraoun ◽  
Zoubir Dahmani
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Stability Of Solutions ◽  
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.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

scholarly journals Triangular System of Higher Order Singular Fractional Differential Equations

2021 ◽  
Vol 45 (01) ◽  
pp. 81-101
Author(s):  
AMELE TAIEB ◽  
ZOUBIR DAHMANI
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
High Dimensional ◽  
Dimensional System ◽  
Stability Of Solutions ◽  
Banach Contraction ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
The Banach Contraction Principle

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, we prove an existence result. We also investigate the uniqueness of solution using the Banach contraction principle. Moreover, we study the Ulam-Hyers stability and the generalized-Ulam-Hyers stability of solutions. Some illustrative examples are also presented.

scholarly journals On the stability of solutions of fractional non conformable differential equations

2020 ◽  
Vol 65 (4) ◽  
pp. 495-502
Author(s):  
Paulo M. Guzman ◽  
Luciano M. Lugo Motta Bittencurt ◽  
Juan E. Napoles Valdes
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Method ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Direct Lyapunov Method ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
The Stability

In this note we obtain sufficient conditions under which we can guarantee the stability of solutions of a fractional differential equations of non conformable type and we obtain some fractional analogous theorems of the direct Lyapunov method for a given class of equations of motion.

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