相关论文: New orthogonal hybrid function based numerical met…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the…
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear…
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…
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…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
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…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared…
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…
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…
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…
In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…
In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…