Matlab routines in Duarte Valerio’s toolbox called ninteger (see detail reviewin (Valério, 2005)). Also created in this toolbox was a Simulink block nid for fractional derivative and integral, where the order of derivative/integral and method of its approximation can be selected. 2.3.1 Grü...
MATLABfractional derivativecaputo derivativeriemann liouville derivative.MATLAB is a high level programming tool for technical computing, its application cuts across different sphere of science, engineering, finance, communication, music etc. With the current increase in the use of non-integer order ...
where m is the smallest integer grater than ALPHA and D^ALPHA is the fractional derivative according to the Caputo's definition. FDEFUN is a function handle corresponding to the vector field of the FDE and for a scalar T and a vector Y, FDEFUN(T,Y) must return a column...
The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivative and zero spin. Complex wave variable transformation is used to convert Atangana conformable nonlinear differential equation into an ordinary differential equation. Using the proposed...
In this paper, the Benettin–Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First, it is proved that the considered class of fractional-order systems admits the necessary vari...
Alzahrani, F.S., Abbas, I.A.: Fractional order GL model on thermoelastic interaction in porous media due to pulse heat flux. Geomech. Eng. 23, 217–225 (2020) MATH Google Scholar Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract...
Using NSFD scheme under the concept of fractional order derivative, we approximate the proposed model (2). We use Grünwald-Letnikov approximation for Caputo derivative. About some detail for this scheme, we refer [54], [55], [56], [57], [58]. Since for nonlinear systems the investigation...
The fractional order SIR model with a Holling type II saturated incidence rate and treatment rate are explored in this manuscript in the Caputo order fractional derivative approach. The existence and uniqueness criterion, as well as non-negativity and boundedness of the solution of the new model ha...
Derivative of the fractional-order sliding surface: $$\begin{aligned} \dot {s}&={{\ddot {x}}_1}+{k_1}{{\dot {x}}_1}+{k_2}{D^\alpha }si{g^\beta }({x_1}) \\ &=\frac{{2{n_p}{k_e}}}{J}i - \frac{B}{J}\omega +d - {{\ddot {\theta }}_{ref}}+{k_1...
According to [7], a fractional-order derivative can be defined as follows: (10) Equation (10) was used to first derive h, and then, we set h⟶0 to seek the limit. On the basis of this fractional derivative, KARCI proposed the first type of fractional derivative [1, 3]: (11)...