The fractional natural decomposition method: theories and applications

2016 ◽  
Vol 40 (7) ◽  
pp. 2362-2376 ◽  
Author(s):  
Mahmoud S. Rawashdeh
Keyword(s):  
Decomposition Method ◽  
Natural Decomposition

scholarly journals Solution for fractional forced KdV equation using fractional natural decomposition method

2020 ◽  
Vol 5 (2) ◽  
pp. 798-810 ◽  
Author(s):  
P. Veeresha ◽  
◽  
D. G. Prakasha ◽  
Jagdev Singh ◽  
◽  
...  
Keyword(s):  
Decomposition Method ◽  
Kdv Equation ◽  
Natural Decomposition

scholarly journals Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2326
Author(s):  
Noufe H. Aljahdaly ◽  
Ravi P. Agarwal ◽  
Rasool Shah ◽  
Thongchai Botmart
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Singular Kernel ◽  
Exact Results ◽  
Burgers Equations ◽  
Kernel Operators ◽  
Natural Decomposition

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.

scholarly journals A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Elbadri ◽  
Shams A. Ahmed ◽  
Yahya T. Abdalla ◽  
Walid Hdidi
Keyword(s):  
Decomposition Method ◽  
Kdv Equation ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Coupled Kdv Equation ◽  
A New Technique ◽  
Natural Decomposition ◽  
Made In

In this article, we applied a new technique for solving the time-fractional coupled Korteweg-de Vries (KdV) equation. This method is a combination of the natural transform method with the Adomian decomposition method called the natural decomposition method (NDM). The solutions have been made in a convergent series form. To demonstrate the performances of the technique, two examples are provided.

Solving $$(1+n)$$-Dimensional Fractional Burgers Equation by Natural Decomposition Method

2020 ◽  
Vol 13 (4) ◽  
pp. 368-381
Author(s):  
M. Cherif ◽  
D. Ziane ◽  
A. K. Alomari ◽  
K. Belghaba
Keyword(s):  
Decomposition Method ◽  
Burgers Equation ◽  
Natural Decomposition
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