A numerical solution to conformable fractional order logistic equation

2020 ◽  
Author(s):  
V. Shameema ◽  
M. C. Ranjini
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Logistic Equation

On the Fractional-Order Logistic Equation with Two Different Delays

2011 ◽  
Vol 66 (3-4) ◽  
pp. 223-227 ◽  
Author(s):  
Ahmed M.A. El-Sayed ◽  
Hala A.A El-Saka ◽  
Esam M. El-Maghrabi
Keyword(s):  
Initial Data ◽  
Numerical Solution ◽  
Fractional Order ◽  
Stable Solution ◽  
Logistic Equation ◽  
Predictor Corrector ◽  
Uniformly Stable

The fractional-order logistic equation with the two different delays r1, r2 > 0, Dα x(t) = ρx(t − r1)[1−x(t −r2)], t > 0 and ρ > 0, with the initial data x(t) = x0, t ≤ 0 are considered. The existence of a unique uniformly stable solution is studied and the Adams-type predictor-corrector method is applied to obtain the numerical solution.

scholarly journals Complexity and Chimera States in a Network of Fractional-Order Laser Systems

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 341
Author(s):  
Shaobo He ◽  
Hayder Natiq ◽  
Santo Banerjee ◽  
Kehui Sun
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Bifurcation Diagram ◽  
Fractional Order ◽  
Dynamical Model ◽  
Chimera States ◽  
Laser Systems ◽  
Complexity Algorithm ◽  
Derivative Order

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

NUMERICAL SOLUTION OF A SPACE FRACTIONAL ORDER SOLUTE TRANSPORT SYSTEM

2018 ◽  
Vol 21 (2) ◽  
pp. 145-160
Author(s):  
Shubham Jaiswal ◽  
Manish Chopra ◽  
S. Das
Keyword(s):  
Solute Transport ◽  
Numerical Solution ◽  
Fractional Order ◽  
Transport System

scholarly journals On the fractional-order logistic equation

2007 ◽  
Vol 20 (7) ◽  
pp. 817-823 ◽  
Author(s):  
A.M.A. El-Sayed ◽  
A.E.M. El-Mesiry ◽  
H.A.A. El-Saka
Keyword(s):  
Fractional Order ◽  
Logistic Equation

scholarly journals Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769006 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Logistic Equation ◽  
Iterative Technique ◽  
Uniqueness Of The Solution

In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo–Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.

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