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Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…

Dynamical Systems · Mathematics 2025-02-12 Prashant M. Gade , Sachin Bhalekar , Janardhan Chevala

In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…

Optimization and Control · Mathematics 2007-05-23 L. Dorcak , I. Petras , I. Kostial , J. Terpak

We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…

Dynamical Systems · Mathematics 2026-05-22 Kai Diethelm , Safoura Hashemishahraki

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti

This paper is concerned with a new type of differential game problems of forwardbackward stochastic systems. There are three distinguishing features: Firstly, our game systems are forward-backward doubly stochastic differential equations,…

Optimization and Control · Mathematics 2015-10-09 Eddie C. M. Hui , Hua Xiao

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…

This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of…

Optimization and Control · Mathematics 2007-05-23 L. Dorcak

This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…

One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…

Dynamical Systems · Mathematics 2023-04-26 Divya D. Joshi , Sachin Bhalekar , Prashant M. Gade

We introduce a non-diffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent…

Pattern Formation and Solitons · Physics 2015-06-12 Russ deForest , Andrew Belmonte

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)…

Pattern Formation and Solitons · Physics 2025-09-22 Vasily E. Tarasov

There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…

Numerical Analysis · Mathematics 2016-05-09 Christopher N Angstmann , Bruce I Henry , Anna V McGann

Stability and stabilization analysis of fractional-order linear time-invariant (FO-LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single-order equivalent…

Systems and Control · Computer Science 2018-08-30 Pouya Badri , Mahdi Sojoodi

In this paper, we investigate the problem of robust Reconfigurable Intelligent Surface (RIS) phase-shifts configuration over heterogeneous communication environments. The problem is formulated as a distributed learning problem over…

Machine Learning · Computer Science 2023-06-05 Charbel Bou Chaaya , Sumudu Samarakoon , Mehdi Bennis

Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…

General Physics · Physics 2014-08-26 S. S. Bayin , J. P. Krisch

In this paper, an attempt is made to understand the dynamics of a fractional order three species Leslie-Gower predator prey food chain model with simplified Holling type IV functional response by considering fractional derivative in Caputo…

Dynamical Systems · Mathematics 2024-01-30 Shuvojit Mondal , Nandadulal Bairagi

Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…

Dynamical Systems · Mathematics 2025-03-18 Cypres Verbeeck , Nikolaos Sfakianakis

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…

Numerical Analysis · Mathematics 2025-10-20 Leszczynski Jacek , Ciesielski Mariusz

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…

Chaotic Dynamics · Physics 2018-04-02 Vasily E. Tarasov , George M. Zaslavsky

Rock-Paper-Scissors (RPS), a game of cyclic dominance, is not merely a popular children's game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no…

Physics and Society · Physics 2019-03-15 Hai-Jun Zhou
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