Results 271 to 280 of about 5,172 (299)

Application to Ordinary Fractional Differential Equations

2019
The numerical approximation of classical ordinary differential equations is relatively simple and, being a focus of mathematical studies for the last few decades, has been by now almost completely investigated. However, a fractional case is much less studied and is still poorly understood despite the fact that there has been a growing interest in the ...
Kolade M. Owolabi, Abdon Atangana
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Generalized boundary problemfor an ordinary differential equation of fractional order

Челябинский физико-математический журнал, 2022
Summary: For an ordinary differential equation of fractional order, a problem with general conditions is formulated and solved. A representation of a solution of the problem under study is found. The uniqueness theorem of a solution is proved. The boundary conditions are given in the form of linear functionals, which allows us to cover a fairly wide ...
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Legendre Collocation Solution to Fractional Ordinary Differential Equations

Applied Mechanics and Materials, 2014
In this paper, we propose an efficient numerical method for ordinary differential equation with fractional order, based on Legendre-Gauss-Radau interpolation, which is easy to be implemented and possesses the spectral accuracy. We apply the proposed method to multi-order fractional ordinary differential equation.
Ting Gang Zhao, Zi Lang Zhan, Jin Xia Huo, Zi Guang Yang   +3 more
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A high-order numerical scheme for the impulsive fractional ordinary differential equations

International Journal of Computer Mathematics, 2017
ABSTRACTIn this paper, we use a good technique to construct a high-order numerical scheme for the impulsive fractional ordinary differential equations (IFODEs). This technique is based on the so-called block-by-block method, which is a common method for the integral equations.
Junying Cao, Lizhen Chen, Ziqiang Wang
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A GENERAL COMPARISON PRINCIPLE FOR CAPUTO FRACTIONAL-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Fractals, 2020
In this paper, we work on a general comparison principle for Caputo fractional-order ordinary differential equations. A full result on maximal solutions to Caputo fractional-order systems is given by using continuation of solutions and a newly proven formula of Caputo fractional derivatives.
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An approximate solution method for ordinary fractional differential equations with the Riemann–Liouville fractional derivatives

Communications in Nonlinear Science and Numerical Simulation, 2014
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Naimark Problem for an Ordinary Differential Equation with a Fractional Discrete Distributed Differentiation Operator

Differential Equations
For an ordinary differential equation with a fractional discretely distributed differentiation operator, the Naimark problem is studied, where the boundary conditions are specified in the form of linear functionals. This allows us to cover a fairly wide class of linear local and nonlocal conditions.
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Fractional ordinary differential equations

2023
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Fractional-Order Ordinary Differential Equations: Theory and Applications

International Journal of Creative and Open Research in Engineering and Management
Fractional calculus extends classical calculus by allowing differentiation and integration of arbitrary real or complex order. Fractional-order ordinary differential equations (FODEs) have become an important mathematical tool for modelling systems with memory and hereditary characteristics.
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Fractional Ordinary Differential Equations in Banach Spaces

2023
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