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Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
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…
In this work, we introduce a new three-dimensional chaotic differential dynamical system. We find equilibrium points of this system and provide the stability conditions for various fractional orders. Numerical simulations will be used to…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
The Proportional-Integral-Derivative Controller is widely used in industries for process control applications. Fractional-order PID controllers are known to outperform their integer-order counterparts. In this paper, we propose a new…
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…
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…
This paper reviews research that studies the principle of self-support (PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time. The existing PSS approach focuses on practical tracking…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
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.…
The article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models viz. Fractional continuously variable order mass-spring damper systems. Here, we use the…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
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…
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…