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In this work, the optimal perturbation iteration method is briefly presented and employed for solving nonlinear Volterra‐Fredholm integral equations. The classical form of the optimal perturbation iteration method is modified, and new algorithms are constructed for integral equations. Comparing our new algorithms with some earlier papers proved the excellent accuracy of the newly proposed technique. [ABSTRACT FROM AUTHOR]

Abstract Chua’s circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua’s circuit is obtained by transforming the classical model of Chua’s circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua’s circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operators.

In this article, a new technique is used to solve the nonlinear boundary value problem of a cantilever‐type nanoelectromechanical system. The technique is called the optimal perturbation iteration method and it is used to solve the problem in the form of a nonlinear differential equation with negative power‐law nonlinearity. A convergence and error estimation of the proposed method is presented proving that the method is convergent. Results for the application of the proposed technique are demonstrated through two examples and the tables and figures prove that the method is efficient and straightforward. [ABSTRACT FROM AUTHOR]

The Allen‐Cahn model equation is extended to the fractional form by using Atangana‐Baleanu derivative. The modified nonlinear equation is analyzed via optimal perturbation iteration technique and Laplace transform. Some new analytical approximate solutions are derived for different cases of order α. Absolute residual errors of different order of approximations are presented to check the effectiveness and power of the proposed method and new derivative. [ABSTRACT FROM AUTHOR]

Chua's circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua's circuit is obtained by transforming the classical model of Chua's circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua's circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operators. [ABSTRACT FROM AUTHOR]

In this work, a mathematical model for the human immunodeficiency virus (HIV) infection of CD4+ T-cells by using the optimal perturbation iteration method (OPIM) is analyzed. Optimization and classical perturbation techniques are combined to build the new proposed method. The iteration algorithm for systems of nonlinear differential equations for this optimal perturbation iteration technique is constructed for the first time. A test problem has been solved and some plots are given to show the reliability and efficiency of the proposed method. Obtained results exhibit the effectiveness and accuracy of the semi-analytical technique. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature.

In this study, we present the new approximate solutions of the nonlinear Klein-Gordon equations via perturbation iteration technique and newly developed optimal perturbation iteration method. Some specific examples are given and obtained solutions are compared with other methods and analytical results to confirm the good accuracy of the proposed methods.We also discuss the convergence of the optimal perturbation iteration method for partial differential equations. The results reveal that perturbation iteration techniques, unlike many other techniques in literature, converge rapidly to exact solutions of the given problems at lower order of approximations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature. [ABSTRACT FROM AUTHOR]

Lane-Emden type equations are nonlinear differential equations which represent many scientific phenomena in astrophysics and mathematical physics. In this study, a new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for Lane-Emden type equations. [ABSTRACT FROM AUTHOR]

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to the generalized regularized long wave equations with a new fractional operator to obtain new approximate solutions. We transform the classical generalized regularized long wave equations to fractional differential form by using the Atangana-Baleanu fractional derivative which is defined with the Mittag-Leffler function. To show the efficiency of the proposed method, a numerical example is given for different values of physical parameters. [ABSTRACT FROM AUTHOR]

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers' equation. The classical damped Burgers' equation is remodeled to fractional differential form via the Atangana–Baleanu fractional derivatives described with the help of the Mittag–Leffler function. To display the efficiency of the proposed optimal perturbation iteration technique, an extended example is deeply analyzed. [ABSTRACT FROM AUTHOR]

In this work, we propose a new optimal perturbation iteration method for solving the generalized Fitzhugh–Nagumo equation with time-dependent coefficients. This research reveals that the new proposed technique, with the aid of symbolic computations, provides a straightforward and impressive mathematical tool for solving nonlinear partial differential equations. Implementing this method to Fitzhugh–Nagumo equation illustrates its potency. Convergence analysis also shows that OPIM, unlike many other methods in literature, converges fast to exact analytical solutions of the nonlinear problems at lower order of approximations. • We proposed a new efficient technique, optimal perturbation iteration technique, as an alternative method to some-well known methods in solving NPDEs. • The presented method has been favorably implemented to obtain the solution of the nonlinear generalized Fitzhugh–Nagumo equations. • Two illustration displays that the OPIM is forceful and prepotent mathematical tool to handle with these types of nonlinear equations. In this technique, it is basically crucial to get the parameters P0; P1; ::: and this makes OPIM time consuming, particularly for large n. • After first three iterations, we encounter a problem of high cost of calculations that takes up computer's memory. However, we have also witnessed that this technique converges fast at lower order of approximations for the nonlinear problems in this study. • Additionally, since the method is frequently toilsome to struggle by hand, one has to use a symbolic computer program to find approximate solutions. In this paper, we have used Mathematica 9.0 to carry out the complex computations in examples. It should be also said that one can get better solutions with more powerful processors or computers. [ABSTRACT FROM AUTHOR]