scholarly journals Ulam stability and data dependence for fractional differential equations with Caputo derivative

2011 ◽  
pp. 1-10 ◽  
Author(s):  
JinRong Wang ◽  
Linli Lv ◽  
Yong Zhou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Caputo Derivative ◽  
Data Dependence ◽  
Ulam Stability ◽  
Fractional Differential

scholarly journals Ulam stability for delay fractional differential equations with a generalized Caputo derivative

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5265-5274 ◽  
Author(s):  
Raad Ameen ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Ulam Stability ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Equations With Delay ◽  
Rassias Stability

The objective of this paper is to extend Ulam-Hyers stability and Ulam-Hyers-Rassias stability theory to differential equations with delay and in the frame of a certain class of a generalized Caputo fractional derivative with dependence on a kernel function. We discuss the conditions such delay generalized Caputo fractional differential equations should satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To demonstrate our results two examples are presented.

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 Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

scholarly journals A Spectral Deferred Correction Method for Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jia Xin ◽  
Jianfei Huang ◽  
Weijia Zhao ◽  
Jiang Zhu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Caputo Derivative ◽  
Numerical Solutions ◽  
Computational Cost ◽  
Correction Method ◽  
Initial Value ◽  
Deferred Correction ◽  
Fractional Differential ◽  
Spectral Deferred Correction

A spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDEs without the penalty of a huge computational cost due to the nonlocality of Caputo derivative. Finally, preliminary numerical experiments are given to verify the efficiency and accuracy of this method.

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