Faedo–Galerkin approximate solutions of a neutral stochastic fractional differential equation with finite delay

2019 ◽  
Vol 347 ◽  
pp. 238-256 ◽  
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey ◽  
Dhirendra Bahuguna
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sameer Qasim Hasan ◽  
Moataz Abbas Holel

The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method.


Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1479
Author(s):  
Jorge Sanchez-Ortiz ◽  
Omar U. Lopez-Cresencio ◽  
Francisco J. Ariza-Hernandez ◽  
Martin P. Arciga-Alejandre

In this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given.


2020 ◽  
Vol 21 (1) ◽  
pp. 7-14
Author(s):  
Dian Nuryani ◽  
Endang Rusyaman ◽  
Betty Subartini

Riccati's Fractional Differential Equation (RFDE) has become a topic of study for researchers because RFDE can model variety of phenomenon in science such as random processes, optimal control and diffusion problems. Phenomena that can be modeled in a mathematical form can make it easier for humans to analyze several things from that phenomenon. RFDE generally does not have an exact solution, therefore a numerical approach solution is needed, one of the methods that gives good accuracy to the actual or exact solution is Polynomial Least Squares, where the errors calculated based on mean absolute percentage error (MAPE) produce a percentage below 1%. In addition, the convergence of a sequence from approximate solutions indicates that the sequence will converge to a solution.


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