Using a numerical method by omitting discretization of data to study numerical solutions for boundary value problems of fractional order differential equations

2019 ◽  
Vol 42 (18) ◽  
pp. 6944-6959 ◽  
Author(s):  
Kamal Shah
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Numerical Method ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Fractional Order Differential Equations

scholarly journals Mild solution of fractional order differential equations with not instantaneous impulses

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Pei-Luan Li ◽  
Chang-Jin Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Mild Solution ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Order Differential Equations

AbstractIn this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.

scholarly journals Iterative numerical method for fractional order two-point boundary value problems

2021 ◽  
Vol 38 (1) ◽  
pp. 47-55
Author(s):  
ALEXANDRU MIHAI BICA ◽  
Keyword(s):  
Differential Equations ◽  
Error Estimate ◽  
Boundary Value Problems ◽  
Numerical Method ◽  
Fractional Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Boundary Problems ◽  
Numerical Example

In this paper we develop an iterative numerical method based on Bernstein splines for solving two-point boundary problems associated to differential equations of fractional order $\alpha\in\left( 0,1\right) $. The convergence of the method is proved by providing the error estimate and it is tested on a numerical example.

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