On the concept of exact solution for nonlinear differential equations of fractional-order

2016 ◽  
Vol 39 (14) ◽  
pp. 4035-4043 ◽  
Author(s):  
Ozkan Guner ◽  
Ahmet Bekir
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Nonlinear Differential Equations

Marine Pipeline Analysis Based on Newton’s Method With an Arctic Application

1970 ◽  
Vol 92 (4) ◽  
pp. 827-833 ◽  
Author(s):  
D. W. Dareing ◽  
R. F. Neathery
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Newton’S Method ◽  
Finite Differences ◽  
Newton's Method ◽  
Nonlinear Differential Equations ◽  
Bending Moments ◽  
Iterative Solutions ◽  
Linear Differential ◽  
Pipe Deflection

Newton’s method is used to solve the nonlinear differential equations of bending for marine pipelines suspended between a lay-barge and the ocean floor. Newton’s method leads to linear differential equations, which are expressed in terms of finite differences and solved numerically. The success of Newton’s method depends on initial trial solutions, which in this paper are catenaries. Iterative solutions converge rapidly toward the exact solution (pipe deflection) even though large bending moments exist in the pipe. Example calculations are given for a 48-in. pipeline suspended in 300 ft of water.

A high-order predictor-corrector method for solving nonlinear differential equations of fractional order

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Thien Binh Nguyen ◽  
Bongsoo Jang
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Prediction Method ◽  
High Order ◽  
New Class ◽  
Accuracy Order ◽  
Predictor Corrector ◽  
Uniform Accuracy

AbstractAn accurate and efficient new class of predictor-corrector schemes are proposed for solving nonlinear differential equations of fractional order. By introducing a new prediction method which is explicit and of the same accuracy order as that of the correction stage, the new schemes achieve a uniform accuracy order regardless of the values of fractional order

scholarly journals Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order

2021 ◽  
Vol 7 (1) ◽  
pp. 723-755
Author(s):  
M. Manigandan ◽  
◽  
Subramanian Muthaiah ◽  
T. Nandhagopal ◽  
R. Vadivel ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Existence Results ◽  
Numerical Examples ◽  
Differential Equations And Inclusions ◽  
Derivatives Of

<abstract><p>In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.</p></abstract>

Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

2018 ◽  
Vol 15 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Musa R. Gad-Allah ◽  
Tarig M. Elzaki
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear Differential

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

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