scholarly journals On the Stability of Fractional Differential Equations Involving Generalized Caputo Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Minh Duc Tran ◽  
Vu Ho ◽  
Hoa Ngo Van
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Fractional Differential ◽  
The Stability ◽  
The Given

This work presents the results of the global existence for fractional differential equations involving generalized Caputo derivative with the case of the fractional order derivative α∈1,2. In addition, the Ulam–Hyers–Mittag-Leffler stability of the given problems is also established.

scholarly journals A Note on the Stability Analysis of Fuzzy Nonlinear Fractional Differential Equations Involving the Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Direct Method ◽  
Stability Result ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.

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 Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Khalid Hattaf
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Lyapunov Direct Method ◽  
Science And Engineering ◽  
Fractional Differential ◽  
The Stability

This paper aims to study the stability of fractional differential equations involving the new generalized Hattaf fractional derivative which includes the most types of fractional derivatives with nonsingular kernels. The stability analysis is obtained by means of the Lyapunov direct method. First, some fundamental results and lemmas are established in order to achieve the goal of this study. Furthermore, the results related to exponential and Mittag–Leffler stability existing in recent studies are extended and generalized. Finally, illustrative examples are presented to show the applicability of our main results in some areas of science and engineering.

scholarly journals On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms

2020 ◽  
Vol 40 (2) ◽  
pp. 227-239
Author(s):  
John R. Graef ◽  
Said R. Grace ◽  
Ercan Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Nonoscillatory Solutions ◽  
Fractional Differential

This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form \[^{C}D_{c}^{\alpha}y(t)+f(t,x(t))=e(t)+k(t)x^{\eta}(t)+h(t,x(t)),\] where \(t\geq c \geq 1\), \(\alpha \in (0,1)\), \(\eta \geq 1\) is the ratio of positive odd integers, and \(^{C}D_{c}^{\alpha}y\) denotes the Caputo fractional derivative of \(y\) of order \(\alpha\). The cases \[y(t)=(a(t)(x^{\prime}(t))^{\eta})^{\prime} \quad \text{and} \quad y(t)=a(t)(x^{\prime}(t))^{\eta}\] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.

scholarly journals Analytic Approach for Solving System of Fractional Differential Equations

2021 ◽  
Vol 32 (1) ◽  
pp. 14
Author(s):  
Nabaa N Hasan ◽  
Zainab John
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Initial Conditions ◽  
Analytic Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

In this paper, Sumudu transformation (ST) of Caputo fractional derivative formulae are derived for linear fractional differential systems. This formula is applied with Mittage-Leffler function for certain homogenous and nonhomogenous fractional differential systems with nonzero initial conditions. Stability is discussed by means of the system's distinctive equation.

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