scholarly journals Bandwidth optimization of information application system under fine integral method of fuzzy fractional order ordinary differential equations

2020 ◽  
Vol 59 (4) ◽  
pp. 2793-2801
Author(s):  
Sixing Huang ◽  
Pengcheng Wei ◽  
Beaufort Hualaitu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Integral Method ◽  
Application System ◽  
Bandwidth Optimization

scholarly journals Solution of Fractional Autonomous Ordinary Differential Equations

2021 ◽  
Author(s):  
Rami AlAhmad ◽  
Qusai AlAhmad ◽  
Ahmad Abdelhadi
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Singular Kernel ◽  
Autonomous Differential Equations ◽  
Implicit Analytical Solution

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

scholarly journals F-Expansion Method and Its Application for Finding Exact Analytical Solutions of Fractional order RLW Equation

2021 ◽  
Author(s):  
Attia Rani ◽  
Qazi Mahmood Ul-Hassan ◽  
Muhammad Ashraf ◽  
Jamshad Ahmad
Keyword(s):  
Solitary Wave ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Nonlinear Partial Differential Equation ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Partial Differential ◽  
Wave Solutions ◽  
Rlw Equation

Exact nonlinear partial differential equation solutions are critical for describing new complex characteristics in a variety of fields of applied science. The aim of this research is to use the F-expansion method to find the generalized solitary wave solution of the regularized long wave (RLW) equation of fractional order. Fractional partial differential equations can also be transformed into ordinary differential equations using fractional complex transformation and the properties of the modified Riemann–Liouville fractional-order operator. Because of the chain rule and the derivative of composite functions, nonlinear fractional differential equations (NLFDEs) can be converted to ordinary differential equations. We have investigated various set of explicit solutions with some free parameters using this approach. The solitary wave solutions are derived from the moving wave solutions when the parameters are set to special values. Our findings show that this approach is a very active and straightforward way of formulating exact solutions to nonlinear evolution equations that arise in mathematical physics and engineering. It is anticipated that this research will provide insight and knowledge into the implementation of novel methods for solving wave equations.

A GENERAL COMPARISON PRINCIPLE FOR CAPUTO FRACTIONAL-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050070 ◽  
Author(s):  
CONG WU
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Comparison Principle ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Fractional Order Systems ◽  
Caputo Fractional Derivatives ◽  
Full Result

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. Based on this result and the formula, we prove a general fractional comparison principle under very weak conditions, in which only the Caputo fractional derivative is involved. This work makes up deficiencies of existing results.

Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation

2019 ◽  
Vol 22 (5) ◽  
pp. 1321-1350 ◽  
Author(s):  
Matthias Hinze ◽  
André Schmidt ◽  
Remco I. Leine
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Benchmark Problems ◽  
State Representation ◽  
Weakly Singular Kernel ◽  
Integration Interval ◽  
Novel Approach ◽  
Infinite State

Abstract In this paper, we propose a novel approach for the numerical solution of fractional-order ordinary differential equations. The method is based on the infinite state representation of the Caputo fractional differential operator, in which the entire history of the state of the system is considered for correct initialization. The infinite state representation contains an improper integral with respect to frequency, expressing the history dependence of the fractional derivative. The integral generally has a weakly singular kernel, which may lead to problems in numerical computations. A reformulation of the integral generates a kernel that decays to zero at both ends of the integration interval leading to better convergence properties of the related numerical scheme. We compare our method to other schemes by considering several benchmark problems.

Legendre Collocation Solution to Fractional Ordinary Differential Equations

2014 ◽  
Vol 687-691 ◽  
pp. 601-605
Author(s):  
Ting Gang Zhao ◽  
Zi Lang Zhan ◽  
Jin Xia Huo ◽  
Zi Guang Yang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Fractional Order ◽  
Numerical Results ◽  
Spectral Accuracy ◽  
Collocation Solution

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. Numerical results demonstrate the effectiveness of the approach.

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