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The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…
The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to single Stokes pulse. The dynamic behavior for this fractional model (called the fractional Stokes system) is investigated,…
The modified Hunter--Saxton equation models the propagation of short capillary-gravity waves. As it involves a mixed derivative, its initial value problem on the periodic domain is much more complicated than the standard evolutionary…
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…
The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…
This paper establishes integral representations of mild solutions of impulsive Hilfer fractional differential equations with impulsive conditions and fluctuating lower bounds at impulsive points. Further, the paper provides sufficient…
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic…
In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural (integer-order) ordinary differential equation (ODE) models…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
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 several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…
This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order {\alpha} . Expressions for the expansions of the evolution operators in powers of the…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
In this paper, we give a criterion on instability of an equilibrium of nonlinear Caputo fractional differential systems. More precisely, we prove that if the spectrum of the linearization has at least one eigenvalue in the sector…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…