Related papers: Fractional dynamical systems defined on fractional…

We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…

Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the…

There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical…

Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective,…

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…

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…

In this article, we employ a fractional version of the radius of curvature in Euler's equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that…

This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…

We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity…

Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…

In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…

This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.

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,…

The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…

Based on the Riemann- and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed…

Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…

Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and…

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…