scholarly journals Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Gaston N’Guérékata
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Banach Contraction ◽  
Fractional Differential ◽  
The Banach Contraction Principle ◽  
Stability Results ◽  
Rassias Stability ◽  
Implicit Fractional Differential Equations

This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems.

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 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 nonlinear implicit differential equations with Riemann-Liouville fractional derivative

2019 ◽  
Vol 52 (1) ◽  
pp. 437-450 ◽  
Author(s):  
Mouffak Benchohra ◽  
Soufyane Bouriah ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Banach Contraction ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
The Stability ◽  
The Banach Contraction Principle ◽  
Implicit Fractional Differential Equations

AbstractIn this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

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