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This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…
We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
We investigate the properties of some recently developed variable-order differential operators involving order transition functions of exponential type. Since the characterisation of such operators is performed in the Laplace domain it is…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
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…
In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…
Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with $T$-periodic coefficients, we can apply a, possibly complex,…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…
Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…
Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…
We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…
The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
Fractional-order dynamical systems were recently introduced in the field of pharmacokinetics where they proved powerful tools for modeling the absorption, disposition, distribution and excretion of drugs which are liable to anomalous…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…