The numerical solution of fractional differential equations using the Volterra integral equation method based on thin plate splines

2018 ◽  
Vol 35 (4) ◽  
pp. 1391-1408 ◽  
Author(s):  
Pouria Assari ◽  
Salvatore Cuomo
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Thin Plate ◽  
Fractional Differential Equations ◽  
Volterra Integral Equation ◽  
Integral Equation Method ◽  
Equation Method ◽  
Thin Plate Splines ◽  
Fractional Differential

Numerical solution of fractional differential equations via a Volterra integral equation approach

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Shahrokh Esmaeili ◽  
Mostafa Shamsi ◽  
Mehdi Dehghan
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Volterra Integral Equation ◽  
Equation Approach ◽  
Algebraic Equations ◽  
Integral Equation Approach ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
The Given

AbstractThe main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.

scholarly journals The General Solution of Differential Equations with Caputo-Hadamard Fractional Derivatives and Noninstantaneous Impulses

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Xianzhen Zhang ◽  
Zuohua Liu ◽  
Hui Peng ◽  
Xianmin Zhang ◽  
Shiyong Yang
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
General Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Order System ◽  
Impulsive Systems ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

Based on some recent works about the general solution of fractional differential equations with instantaneous impulses, a Caputo-Hadamard fractional differential equation with noninstantaneous impulses is studied in this paper. An equivalent integral equation with some undetermined constants is obtained for this fractional order system with noninstantaneous impulses, which means that there is general solution for the impulsive systems. Next, an example is given to illustrate the obtained result.

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