scholarly journals Novel Stability Results for Caputo Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Abdellatif Ben Makhlouf ◽  
El-Sayed El-Hady
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Mortality Rates ◽  
Exact Analytical Solutions ◽  
Scientific Investigations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Stability Results

Modelling some diseases with large mortality rates worldwide, such as COVID-19 and cancer is crucial. Fractional differential equations are being extensively used in such modelling stages. However, exact analytical solutions for the solutions of such kind of equations are not reachable. Therefore, close exact solutions are of interests in many scientific investigations. The theory of stability in the sense of Ulam and Ulam–Hyers–Rassias provides such close exact solutions. So, this study presents stability results of some Caputo fractional differential equations in the sense of Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias. Two examples are introduced at the end to show the validity of our results. In this way, we generalize several recent interesting results.

scholarly journals Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Adel Al-Rabtah ◽  
Shaher Momani ◽  
Mohamed A. Ramadan
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Spline Functions ◽  
Exact Analytical Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Good Agreement

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for0<α≤1andα≥1, whereαdenotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.

scholarly journals Novel stability results for Caputo fractional differential equations

2020 ◽  
Author(s):  
El-sayed El-hady ◽  
El-Sayed El ◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Stability Results

The aim of this article is to present stability results of some Caputo fractional differential equations in the sense of Ulam-Hyers, Ulam-Hyers-Rassias and generalized Ulam-Hyers-Rassias. In this way, we generalize some recent interesting results.

Caputo fractional differential equations with non-instantaneous impulses and strict stability by Lyapunov functions

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5217-5239 ◽  
Author(s):  
Ravi Agarwal ◽  
Snehana Hristova ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Intervals ◽  
Dini Derivative ◽  
Comparison Results ◽  
Strict Stability ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional differential equations with non-instantaneous impulses is presented. Comparison results using this definition and scalar fractional differential equations with non-instantaneous impulses are presented and sufficient conditions for strict stability and uniform strict stability are given. Examples are given to illustrate the theory.

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 Exact solutions of conformable fractional differential equations

2021 ◽  
Vol 22 ◽  
pp. 103916
Author(s):  
Haleh Tajadodi ◽  
Zareen A. Khan ◽  
Ateeq ur Rehman Irshad ◽  
J.F. Gómez-Aguilar ◽  
Aziz Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Fractional Differential
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