Related papers: Fractional order logistic map; Numerical approach
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order $1<\alpha<2$ considered on a cylinder. We consider relatively large values of the nonlinearity parameter $K$ for…
The separation dimension of a graph $G$, written $\pi(G)$, is the minimum number of linear orderings of $V(G)$ such that every two nonincident edges are "separated" in some ordering, meaning that both endpoints of one edge appear before…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
In this paper, a multi-class Aw-Rascle \textrm{(AR)} model with time fractional order derivative is presented. The conservative form of the proposed model is considered for the natural extension and generalization of equations involved. The…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…
The simple continued fractions for the Golden & Silver means are well-known. It is astonishing that, as far as we know, no one has published half-iterates (let alone quarter-iterates) for the corresponding algorithms. We also examine the…
A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type…
As it is known various dynamical processes can be modeled through the systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces with determining the adequate orders of time-fractional…
In this paper the linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 less than or equal to nu which is less than or equal…
We are studying fractional linear recursions of second and third orders and finding periodic recursions with periods of eight and twelve, which, apparently, were not known before.
Many natural and social systems possess power-law memory, and their mathematical modeling requires the application of discrete and continuous fractional calculus. Most of these systems are nonlinear and demonstrate regular and chaotic…
This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within…