scholarly journals Short memory principle and a predictor–corrector approach for fractional differential equations

2007 ◽  
Vol 206 (1) ◽  
pp. 174-188 ◽  
Author(s):  
Weihua Deng
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Short Memory ◽  
Fractional Differential ◽  
Short Memory Principle ◽  
Predictor Corrector

Dynamics of generalized Caputo type delay fractional differential equations using a modified Predictor-Corrector scheme

2021 ◽  
Vol 96 (12) ◽  
pp. 125213
Author(s):  
Zaid Odibat ◽  
Vedat Suat Erturk ◽  
Pushpendra Kumar ◽  
V Govindaraj
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Differential ◽  
Predictor Corrector

Fractional impulsive differential equations: Exact solutions, integral equations and short memory case

2019 ◽  
Vol 22 (1) ◽  
pp. 180-192 ◽  
Author(s):  
Guo–Cheng Wu ◽  
De–Qiang Zeng ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Impulsive Differential Equations ◽  
Fundamental Solutions ◽  
Impulsive Conditions ◽  
Short Memory ◽  
Fractional Differential ◽  
Piecewise Functions

Abstract Fractional impulsive differential equations are revisited first. Some fundamental solutions of linear cases are given in this study. One straightforward technique without using integral equation is adopted to obtain exact solutions which are given by use of piecewise functions. Furthermore, a class of short memory fractional differential equations is proposed and the variable case is discussed. Mittag–Leffler solutions with impulses are derived which both satisfy the equations and impulsive conditions, respectively.

Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hua Kong ◽  
Guo-Cheng Wu ◽  
Hui Fu ◽  
Kai-Teng Wu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Numerical Solutions ◽  
Linear Interpolation ◽  
Relaxation Equation ◽  
Fractional Integral Equation ◽  
Generalized Fractional Integral ◽  
Fractional Differential ◽  
Predictor Corrector

Abstract A new class of fractional differential equations with exponential memory was recently defined in the space A C δ n [ a , b ] $A{C}_{\delta }^{n}\left[a,b\right]$ . In order to use the famous predictor–corrector method, a new quasi-linear interpolation with a non-equidistant partition is suggested in this study. New Euler and Adams–Moulton methods are proposed for the fractional integral equation. Error estimates of the generalized fractional integral and numerical solutions are provided. The predictor–corrector method for the new fractional differential equation is developed and numerical solutions of fractional nonlinear relaxation equation are given. It can be concluded that the non-equidistant partition is needed for non-standard fractional differential equations.

A predictor–corrector scheme for solving nonlinear fractional differential equations with uniform and nonuniform meshes

2019 ◽  
Vol 10 (05) ◽  
pp. 1950033
Author(s):  
Mohammad Javidi ◽  
Mahdi Saedshoar Heris ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlinear Fractional Differential Equations ◽  
Area Distribution ◽  
Nonuniform Meshes ◽  
Equidistributing Meshes ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Predictor Corrector ◽  
Equal Height

In this paper, we develop two algorithms for solving linear and nonlinear fractional differential equations involving Caputo derivative. For designing new predictor–corrector (PC) schemes, we select the mesh points based on the two equal-height and equal-area distribution. Furthermore, the error bounds of PC schemes with uniform and equidistributing meshes are obtained. Finally, examples are constructed for illustrating the obtained PC schemes with uniform and equidistributing meshes. A comparative study is also presented.

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