Based on BP nerve Research on the Stability Criterion of Fractional Differential Equations of Network Algorithm

2020 ◽  
Vol 29 (3) ◽  
Author(s):  
Yutian Ma ◽  
Wenwen Li
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Stability Criterion ◽  
Network Algorithm ◽  
Fractional Differential ◽  
The Stability

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 Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

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 Qualitative Analysis of Implicit Dirichlet Boundary Value Problem for Caputo-Fabrizio Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Rozi Gul ◽  
Muhammad Sarwar ◽  
Kamal Shah ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Differential Equations ◽  
Qualitative Analysis ◽  
Fractional Differential Equations ◽  
Dirichlet Boundary ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Dirichlet Boundary Conditions ◽  
Fractional Differential ◽  
The Stability ◽  
Implicit Fractional Differential Equations

This article studies a class of implicit fractional differential equations involving a Caputo-Fabrizio fractional derivative under Dirichlet boundary conditions (DBCs). Using classical fixed-point theory techniques due to Banch’s and Krasnoselskii, a qualitative analysis of the concerned problem for the existence of solutions is established. Furthermore, some results about the stability of the Ulam type are also studied for the proposed problem. Some pertinent examples are given to justify the results.

scholarly journals Cubic Spline Collocation Method for Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Shui-Ping Yang ◽  
Ai-Guo Xiao
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Cubic Spline ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Fractional Differential ◽  
Cubic Spline Collocation ◽  
The Stability ◽  
Two Parameters

We discuss the cubic spline collocation method with two parameters for solving the initial value problems (IVPs) of fractional differential equations (FDEs). Some results of the local truncation error, the convergence, and the stability of this method for IVPs of FDEs are obtained. Some numerical examples verify our theoretical results.

scholarly journals Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 896
Author(s):  
Snezhana Hristova ◽  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Kuratowski Measure Of Noncompactness ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability ◽  
Existence Criteria

A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the existence of solutions. It leads to the necessity of obtaining existence criteria for a boundary value problem for Hadamard fractional differential equations of variable order. Also, the stability in the sense of Ulam–Hyers–Rassias is investigated. The results are obtained based on the Kuratowski measure of noncompactness. An example illustrates the validity of the observed results.

scholarly journals High order algorithms for numerical solution of fractional differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Shahbazi Asl ◽  
Mohammad Javidi ◽  
Yubin Yan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Algorithms ◽  
Interpolation Polynomial ◽  
High Order ◽  
The Novel ◽  
Fractional Differential ◽  
Novel Algorithms ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.

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.

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.

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