相关论文: The oscillatory solutions of multi-order fractiona…

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…

The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on…

In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…

This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions are for the asymptotic stability of such systems are obtained.

In the paper, the initial-boundary value problems to a semilinear integro-differential equation with multi-term fractional Caputo derivatives are analyzed. A particular case of this equation models oxygen diffusion through capillaries.…

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…

We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the…

In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great…

This paper is devoted to the study of the asymptotic behavior of solutions to multi-order fractional cooperative systems. First, we demonstrate the boundedness of solutions to fractional-order systems under certain conditions imposed on the…

A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…

This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…

We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…

The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…

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…

In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…

In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…

In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…