Internal Bernstein functions and Lévy‐Laplace exponents

2020 ◽  
Author(s):  
Kholoud Basalim ◽  
Safa Bridaa ◽  
Wissem Jedidi
Keyword(s):  
Bernstein Functions

An efficient approximate method for solving two-dimensional fractional optimal control problems using generalized fractional order of Bernstein functions

2020 ◽  
Author(s):  
Ali Ketabdari ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Operational Matrix ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Control Variables ◽  
Fractional Optimal Control ◽  
Bernstein Functions ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract We define a new operational matrix of fractional derivative in the Caputo type and apply a spectral method to solve a two-dimensional fractional optimal control problem (2D-FOCP). To acquire this aim, first we expand the state and control variables based on the fractional order of Bernstein functions. Then we reduce the constraints of 2D-FOCP to a system of algebraic equations through the operational matrix. Now, one can solve straightforward the problem and drive the approximate solution of state and control variables. The convergence of the method in approximating the 2D-FOCP is proved. We demonstrate the efficiency and superiority of the method by comparing the results obtained by the presented method with the results of previous methods in some examples.

Bernstein Functions and the Dirichlet Problem

1989 ◽  
Vol 20 (5) ◽  
pp. 1055-1068 ◽  
Author(s):  
Alan R. Elcrat ◽  
Kirk E. Lancaster
Keyword(s):  
Dirichlet Problem ◽  
Bernstein Functions
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