Multistage Adomian Decomposition Method for Solving NLP Problems Over a Nonlinear Fractional Dynamical System

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Decomposition Method ◽  
Optimization Problem ◽  
Adomian Decomposition Method ◽  
Optimal Solution ◽  
Initial Time ◽  
Adomian Decomposition ◽  
Fractional Differential ◽  
Fractional Dynamical System

This paper deals with implementation of the multistage Adomian decomposition method (MADM) to solve a class of nonlinear programming (NLP) problems, which are reformulated with a nonlinear system of fractional differential equations. The multistage strategy is used to investigate the relation between an equilibrium point of the fractional order dynamical system and an optimal solution of the NLP problem. The preference of the method lies in the fact that the multistage strategy gives this relation in an arbitrary longtime interval, while the Adomian decomposition method (ADM) gives the optimal solution just only in the neighborhood of the initial time. The numerical results taken by the fractional order MADM show that these results are compatible with the solution of NLP problem rather than the ADM. Furthermore, in some cases the fractional order MADM can perform more rapid convergency to the optimal solution of optimization problem than the integer order ones.

HYPERCHAOS IN THE FRACTIONAL-ORDER RÖSSLER SYSTEM WITH LOWEST-ORDER

2009 ◽  
Vol 19 (01) ◽  
pp. 339-347 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Point Of View ◽  
Hyperchaotic System ◽  
Adomian Decomposition ◽  
Rossler System ◽  
Fractional Differential ◽  
Rössler System

This Letter analyzes the hyperchaotic dynamics of the fractional-order Rössler system from a time-domain point of view. The approach exploits the Adomian decomposition method (ADM), which generates series solution of the fractional differential equations. A remarkable finding of the Letter is that hyperchaos occurs in the fractional Rössler system with order as low as 3.12. This represents the lowest order reported in literature for any hyperchaotic system studied so far.

scholarly journals An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

Solutions of the modified Kawahara equation with time-and space-fractional derivatives

2016 ◽  
Vol 7 (1) ◽  
pp. 10 ◽  
Author(s):  
M. Safavi ◽  
A. A. Khajehnasiri
Keyword(s):  
Approximate Solution ◽  
Fractional Differential Equations ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Time And Space ◽  
Kawahara Equation ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we consider fractional differential equations (FDEs), specially modified Kawahara equation with time and space fractional derivatives, also we use Adomian decomposition method (ADM) to approximate the exact solutions of this equation. The ADM method converts the FKEs to an iterated formula that approximate solution is computable. The numerical examples illustrate efficiency and accuracy of the proposed method.

scholarly journals Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

2019 ◽  
Vol 10 (1) ◽  
pp. 122 ◽  
Author(s):  
Hassan Khan ◽  
Umar Farooq ◽  
Rasool Shah ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Form Solution ◽  
Physical Models ◽  
Fractional Partial Differential Equations ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Closed Contact

In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document