Related papers: Computational Methods in the Fractional Calculus o…
Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this paper we introduce a new mathematical tool to solve fractional equations representing models of fractional systems : The Ultradistributions. Ultradistributions permit us to unify the notion of integral and derivative in one only…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
The aim of this work is to give a broad panorama of the control properties of fractional diffusive models from a numerical analysis and simulation perspective. We do this by surveying several research results we obtained in the last years,…
We propose and study an optimal control model for malaria infection described by system of fractional differential equations. The model is formulated in terms of the left and right Caputo fractional derivatives. We determine the necessary…
To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order…
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…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…
The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…