Numerical Simulation of Nonlinear Ecological Models with Nonlocal and Nonsingular Fractional Derivative

2020 ◽  
pp. 303-320
Author(s):  
Kolade M. Owolabi
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Ecological Models

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.

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

NUMERICAL SIMULATION OF FRACTIONAL BIOHEAT EQUATION IN HYPERTHERMIA TREATMENT

2014 ◽  
Vol 14 (02) ◽  
pp. 1450018 ◽  
Author(s):  
R. S. DAMOR ◽  
SUSHIL KUMAR ◽  
A. K. SHUKLA
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Derivative ◽  
Thermal Damage ◽  
Heating Time ◽  
Bioheat Equation ◽  
Hyperthermia Treatment ◽  
Implicit Finite Difference ◽  
Time Fractional Derivative

This paper deals with the study of fractional bioheat equation for hyperthermia treatment in cancer therapy with external electromagnetic (EM) heating. Time fractional derivative is considered as Caputo fractional derivative of order α ∈ (0, 1]. Numerical solution is obtained by implicit finite difference method. The effect of anomalous diffusion in tissue has been studied. The temperature profile and thermal damage over the entire affected region are obtained for different values of α.

Investigation of the wall friction in the pipe induced by the oscillating flow

2008 ◽  
Vol 222 (3) ◽  
pp. 387-392 ◽  
Author(s):  
J H Jia ◽  
J Y Du ◽  
Y Wang ◽  
H X Hua
Keyword(s):  
Numerical Simulation ◽  
Shear Stress ◽  
Fractional Derivative ◽  
Viscoelastic Fluid ◽  
Critical Value ◽  
Wall Friction ◽  
Rheological Parameters ◽  
Oscillating Flow ◽  
Pipe Radius ◽  
Friction Curve

The wall friction induced by the oscillating flow of the fractional derivative Maxwell viscoelastic fluid in the pipe is investigated. The velocity and the shear stress solutions of the flow are solved. The friction is derived from the shear stress expression and analysed by numerical simulation. From analysis, it is found that the friction amplitude exhibits resonance-like phenomena. Moreover, the number of the resonance-like peaks, the enhancement magnitude, and the resonance-like frequency of the same order vary with the pipe radius and rheological parameters of fluids. When the radius overtakes the critical value, the friction curve monotonously decreases, and when the radius is big enough, the enhancement disappears.

Numerical simulation of normal and cancer cells’ populations with fractional derivative under radiotherapy

2020 ◽  
Vol 187 ◽  
pp. 105202 ◽  
Author(s):  
Musiliu Folarin Farayola ◽  
Sharidan Shafie ◽  
Fuaada Mohd Siam ◽  
Ilyas Khan
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Cancer Cells

scholarly journals Numerical simulation of three-dimensional fractional-order convection-diffusion PDEs by a local meshless method

2020 ◽  
pp. 210-210 ◽  
Author(s):  
Mohan Srivastava ◽  
Hijaz Ahmad ◽  
Imtiaz Ahmad ◽  
Phatiphat Thounthong ◽  
Nawaz Khan
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Three Dimensional ◽  
Fractional Part ◽  
Higher Dimensions ◽  
Test Problems ◽  
Numerical Treatment ◽  
Convection Diffusion ◽  
Derivatives Of

In this article, we present an efficient local meshless method for the numerical treatment of three-dimensional convection-diffusion PDEs. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solution on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fractional derivative. Some test problems on regular and irregular computational domains are presented to verify the validity, efficiency and accuracy of the method.

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