Related papers: Fractional Logistic Map
The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical…
Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise naturally in heat transport in materials…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m<n, n>1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
Nonlinear fractional dynamics with scale invariance in continuous and discrete time approaches are described. We use non-integer-order integro-differential operators that can be interpreted as generalizations of scaling (dilation)…
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions…
In this paper we introduce the notion of fractional martingale as the fractional derivative of order $\alpha$ of a continuous local martingale, where $\alpha\in(-{1/2},{1/2})$, and we show that it has a nonzero finite variation of order…
Anew method for finding closed-loop optimal controllers of fractional tracking quadratic optimal control problems is introduced. The optimality conditions for the fractional optimal control problem are obtained. Illustrative examples are…
A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order $\alpha, 0 < \alpha \leq 1$, called $F^\alpha$-integral, is defined, which is suitable to integrate functions with fractal…
For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on…
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…
We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is…
In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…
We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
This paper is concerned with a generalized Halanay inequality and its applications to fractional-order delay linear systems. First, based on a sub-semigroup property of Mittag-Leffler functions, a generalized Halanay inequality is…