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The flow as well as the chemically reactive solute transfer problem in a viscous fluid over an exponentially stretching sheet are analytically investigated in this work. The nonlinear differential equations associated to the motion equations are approximately solved by means of the modified Optimal Homotopy Asymptotic Method (OHAM). The dual approximate analytical solutions are obtained. By comparison with the corresponding numerical solutions a good agreement is performed and show that this procedure is effective, accurate and easy to use in applications. [ABSTRACT FROM AUTHOR]

Enhancing the nanosized‐electrolyte's characteristics in Lithium‐driven micro‐batteries (LIMBs) is indispensable to improve the overall efficiency, security, and lifespan of these energy devices, designing nano‐sized electrolyte with a wide electrochemical stability window while keeping them compatible with electrode materials is one of the improvement goals. Battery technologies must go through this optimization process in order to be used practically. A sensing mechanism to keep an eye on the health of Li‐ion energy devices through the magnetization. Magnetic micro‐fluidic patterns that change could be a sign of battery deterioration or other problems with performance. Li‐ion battery health is one application of magnetic sensing that you can do with magnetic sensing. Battery health variations and other performance problems can be found using magnetic mass transport patterns. Present study examines the effects of magnetic field on Eyring–Powel mass transport in nano‐porous channels over a stretching sheet. The principal equations exhibiting the phenomenon are transformed into non‐linear differential equation by second‐order approximation by using a similarity transformation. Furthermore, a semi‐analytic technique named optimal homotopy asymptotic method (OHAM) is used to solve the transformed Eyring–Powell model. The numerical results demonstrated the impact of variations in velocity, skin‐friction coefficient and Sherwood number for the proposed scheme. [ABSTRACT FROM AUTHOR]

Within the domain of nonlinear dynamics, the Belousov-Zhabotinsky reaction system has consistently captivated researchers, sustaining its position as a vibrant and dynamic area of exploration. As an enduring subject of study, the Belousov-Zhabotinsky system provides continuous opportunities to unravel the foundational tenets of nonlinear dynamics within intricate systems. In our quest to deepen comprehension of this complex system, we introduce an innovative methodology for addressing the time fractional Belousov-Zhabotinsky system. This novel approach leverages both the Natural Transform Iterative Method (NTIM) and the Optimal Homotopy Asymptotic Method (OHAM), aiming to contribute novel insights and methodologies to the ongoing discourse surrounding this intriguing and influential area of research. We obtained a series solution to test the accuracy of the suggested approach. The proposed technique has the advantage of requiring few calculations while producing high-precision results. To help you better understand, 2D and 3D graphical representations are provided to demonstrate the model's behavior and how changing the fractional order derivative in Caputo's sense and time affects the solutions.

Within the domain of nonlinear dynamics, the Belousov-Zhabotinsky reaction system has consistently captivated researchers, sustaining its position as a vibrant and dynamic area of exploration. As an enduring subject of study, the Belousov-Zhabotinsky system provides continuous opportunities to unravel the foundational tenets of nonlinear dynamics within intricate systems. In our quest to deepen comprehension of this complex system, we introduce an innovative methodology for addressing the time fractional Belousov-Zhabotinsky system. This novel approach leverages both the Natural Transform Iterative Method (NTIM) and the Optimal Homotopy Asymptotic Method (OHAM), aiming to contribute novel insights and methodologies to the ongoing discourse surrounding this intriguing and influential area of research. We obtained a series solution to test the accuracy of the suggested approach. The proposed technique has the advantage of requiring few calculations while producing high-precision results. To help you better understand, 2D and 3D graphical representations are provided to demonstrate the model's behavior and how changing the fractional order derivative in Caputo's sense and time affects the solutions. [ABSTRACT FROM AUTHOR]

In this study, a new physical model has been created to look into the behaviour of transient incompressible unsteady flow between two infinite parallel plates exposed to high temperatures. The model takes into consideration thermal radiation flux, chemical reaction, and mass diffusion at the boundaries. To handle non-integer behaviour, the model incorporates the Caputo notion of time fractional derivative. To solve this complex physical fractional order fluid model, a novel optimal homotopy asymptotic method and semi-analytical methodology is extended and utilized successfully. This method provides a third-order highly approximate solution, offering valuable insights into the behaviour within the system. The study comprehensively examines the effects of varied flow characteristics and fractional order on the dynamics of the system. The results are visually presented through graphs, offering a clear understanding of the system's response under different conditions. The effectiveness and ease of use of the optimal homotopy asymptotic method make it a valuable tool for solving boundary value fractional order problems encountered in scientific fields. The developed physical model and its fractional extension contribute significantly to the understanding of unsteady flow phenomena with thermal and chemical effects, advancing knowledge in this area of research. [ABSTRACT FROM AUTHOR]

This paper explores the application of fuzzy theory to solve fractional heat equations using a novel approach, the Optimal Homotopy Asymptotic Method (OHAM). We introduce a semi-analytical method to address fuzzy fractional-order heat equations, aiming to overcome the limitations of existing approaches. Our methodology leverages the generalized Caputo-Katugampola (CK) definition with two parameters α and ρ, to define fractional derivatives. Through this research, we present a comprehensive framework for tackling this challenging problem. To illustrate the effectiveness and feasibility of our method, we provide several practical examples. The results are presented in tables and figures, and our approach is compared to the exact solutions. This study not only contributes to the field but also offers a powerful and efficient way to address fuzzy fractional heat equations with increased accuracy and reduced computational effort. [ABSTRACT FROM AUTHOR]

Fractional derivative gives important tools to fit the real data with mathematical models because of the fractional parameters. This article introduces an algorithm for the approximation of solutions to linear and nonlinear fuzzy fractional initial value problems, specifically those involving the Caputo-Katugampola (CK) derivative, a generalized fractional derivative. The CK fractional derivative, characterized by two parameters, extends the capabilities of Caputo and Caputo-Hadamard fractional derivatives. The Optimal Homotopy Asymptotic Method (OHAM) is employed as an approximate analytic technique, offering multiple convergent control parameters to fine-tune solution convergence and accuracy. The article also addresses the representation of environmental uncertainty within the solution using Zadeh's fuzzy theory extension principle. This algorithm not only introduces the fuzzy fractional differential with the CK derivative but also provides a convergent analytic solution with minimal residual error. This contribution aims to support researchers in refining mathematical models to better align with real-world data. Three examples are considered to demonstrate the efficiency of the algorithm with several figures and tables. [ABSTRACT FROM AUTHOR]

This work focuses on solving and analyzing two-point fuzzy boundary value problems in the form of fractional ordinary differential equations (FFOBVPs) using a new version of the approximation analytical approach. FFOBVPs are useful in describing complex scientific phenomena that include heritable characteristics and uncertainty, and obtaining exact or close analytical solutions for these equations can be challenging, especially in the case of nonlinear problems. To address these difficulties, the optimal homotopy asymptotic method (OHAM) was studied and extended in a new form to solve FFOBVPs. The OHAM is known for its ability to solve both linear and nonlinear fractional models and provides a straightforward methodology that uses multiple convergence control parameters to optimally manage the convergence of approximate series solutions. The new form of the OHAM presented in this work incorporates the concepts of fuzzy sets theory and some fractional calculus principles to include fuzzy analysis in the method. The steps of fuzzification and defuzzification are used to transform the fuzzy problem into a crisp problem that can be solved using the OHAM. The method is demonstrated by solving and analyzing linear and nonlinear FFOBVPs at different values of fractional derivatives. The results obtained using the new form of the fuzzy OHAM are analyzed and compared to those found in the literature to demonstrate the method's efficiency and high accuracy in the fuzzy domain. Overall, this work presents a feasible and efficient approach for solving FFOBVPs using a new form of the OHAM with fuzzy analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate effective and accurate dual analytic approximate solutions, while taking into account thermal effects. The heat and mass transfer problem in a viscous fluid flow are analytically explored by using the modified Optimal Homotopy Asymptotic Method (OHAM). By using similarity transformations, the motion equations are reduced to a set of nonlinear ordinary differential equations. Based on the numerical results, it was revealed that there are dual analytic approximate solutions within the mass transfer problem. The variation of the physical parameters (the Prandtl number and the temperature distribution parameter) over the temperature profile is analytically explored and graphically depicted for the first approximate and the corresponding dual solution, respectively. The advantage of the proposed method arises from using only one iteration for obtaining the dual analytical solutions. The presented results are effective, accurate and in good agreement with the corresponding numerical results with relevance for further engineering applications of heat and mass transfer problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new method to create a series solution to the time-fractional Navier–Stokes equations using a combination of the Laplace transform with the optimal homotopy asymptotic method. Caputo's derivative was applied in the present technique. Three test problems are carried out to validate and demonstrate the method's efficacy. The system has been found to be a very reliable, effective and powerful technique for solving the proposed model as well as a variety of engineering and science problems. [ABSTRACT FROM AUTHOR]

This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the optimal homotopy asymptotic method (OHAM). These represent the ε -approximate OHAM solutions. A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the representative figures. This procedure is suitable to be applied for dynamical systems with certain geometrical properties. [ABSTRACT FROM AUTHOR]

We study here the effectiveness of the optimal homotopy asymptotic method (OHAM) in solving non-linear differential equations of non-Newtonian fluids. To this consequence, we consider the Oldroyd 6-constant fluid when it demonstrates slippage between the plate and fluid generating non-linear boundary value problems. The problems of plane Couette flow, generalized Couette flow, and plane Poiseuille flow are considered. Graphs of the results are plotted to show the performance of the method in terms of velocity profile. It is observed that the method is quite easy to implement, having latent potential to handle such kinds of non-linear problems and yield accurate results at minimum to low computational work.

Recently solving integro-differential equations have been the focus of attention among many researchers in the field of mathematic and engineering. The aim of current study is to apply the well-known optimal homotopy asymptotic method (OHAM) on a specific and famous model of these equations. It is illustrated that auxiliary functions and the number of Taylor series terms affect the accuracy of the solution. Hence, at first a solution has been found with an acceptable error by OHAM. Then, it has been continued to attain a better solution by Multistep optimal homotopy asymptotic method. All these processes had improved the precision of the solution. Auxiliary polynomials of two, three, and four degrees and different numbers of Taylor series term have been investigated to solve a nonlinear system derived by two biological species ‎living together. Ultimately, appropriate results with auxiliary polynomials of degree four and Taylor series with six terms have been obtained precisely. In addition, the error values decrease significantly compared to the other cases.

In this paper, we have explored the steady Poiseuille flow of couple stress fluid between two parallel plates under ‎the influence of non-isothermal effects of Reynold viscosity model, using Optimal Homotopy Asymptotic Method ‎‎(OHAM) and New Iterative Method (NIM). We obtained expressions for velocity profile, temperature distribution, ‎average velocity, volume flux and shear stress. The solutions obtained using these methods are in the form of ‎infinite series; therefore, they can be easily computed. Comparative results of solutions obtained by both methods ‎are given using different tables and graphs.

In this study, the Daftardar–Jeffery polynomials are incorporated in the homotopy of the optimal homotopy asymptotic method (OHAM) for solving the generalized Hirota–Satsuma coupled system of Korteweg–de Vries equations. The results are displayed through graphs and tables. The results obtained in this study are also compared with the published work on OHAM, which shows that OHAM-DJ is more explicit, reliable, and an efficient analytical technique. The exactness of the developed method can be improved by performing the higher iterations.

Nanoparticles are generally used to scatter and absorb solar radiations in nanofluid-based direct solar receivers to efficiently transport and store the heat. However, solar energy absorption in nanofluid can be enhanced by using differential materials and tuning nanofluid parameter. In this regard, theoretical investigations of unsteady homogeneous Hiemenz flow of an incompressible nanofluid having copper and silver nanoparticles over a porous wedge is carried out by using optimal homotopy asymptotic method (OHAM). Hence, a semi-analytical solver is applied to the transformed system to study the significance of magnetic field along with Prandtl number. In this work, impacts of conductive radiations, heat sink/source, unsteadiness, and flow parameters have been investigated for velocity and temperature profiles of copper and silver nanoparticles-based nanofluid. The effects of magnetic strength, volume fraction of nanoparticles, thermal conductivity, and flow parameters have also been studied on the considered nanofluids. [ABSTRACT FROM AUTHOR]

In this work, a nonlinear investigation of non-homogeneous varying thickness circular plates resting on elastic foundations under the influence of the magnetic field is investigated. The non-homogeneity of the circular plates' material is presumed to occur due to linear and parabolic changes in Young's modulus likewise the density along the radial direction in a unique manner. The geometric Von Kármán equations are used in modelling the governing differential equations. The transverse deflection is approximated using an assumed single term mode shape while the central deflection in form of Duffing's equation is obtained using the Galerkin method. Subsequently, the semi-analytical solutions are provided using the Optimal Homotopy Asymptotic Method (OHAM), the analytical solutions are used for parametric investigation. The results in this work are in good harmony with past results in the literature. From the results, it is realized that the nonlinear frequency of the circular plate increases with an increase in the linear elastic foundation. Also, the results showed that clamped edge and simply supported edge condition produced the same hardening nonlinearity. However, varying taper and non-homogeneity lower the nonlinear frequency ratio. Also, maximum deflection occurs when excitation force is zero, and attenuation of deflection is observed due to the presence of a magnetic field, varying thickness, homogeneity, and elastic foundation. It is anticipated that the discoveries from this research will boost the design of structures subjected to vibration. [ABSTRACT FROM AUTHOR]

In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward. [ABSTRACT FROM AUTHOR]

This paper analyses a dynamical system derived from a left-invariant, drift-free optimal control problem on the Lie group SO(3) × ℝ3 × ℝ3 in deep connection with the important role of the Lie groups in tackling the various problems occurring in physics, mathematics, engineering and economic areas [1, 2, 3, 4, 5]. The stability results for the initial dynamics were inconclusive for a lot of equilibrium points (see [6]), so a linear control has been considered in order to stabilize the dynamics. The analytic approximate solutions of the resulting nonlinear system are established and a comparison with the numerical results obtained via the fourth-order Runge-Kutta method is achieved.

This paper analytically investigates the flow as well as the chemically reactive solute transfer problem in a viscous fluid. The motion equations are reduced to a nonlinear ordinary differential equations system using the similarity transformations. The obtained nonlinear differential system is for the first time approximately solved by means of the Optimal Homotopy Asymptotic Method (OHAM). The effects of the partial slip and suction/blowing parameters are analytically analyzed. Some examples are given; the obtained results provides us with a good agreement with the numerical results and reveal that our procedure is effective, accurate and easy to use.

The paper is dealing with stability problems for a nonlinear system on the Lie group SO(3) × R3 × R3. The approximate analytic solutions of the considered system via Optimal Homotopy Asymptotic Method are presented, too.

A comparative study between optimal homotopy asymptotic method (OHAM) and some other well-known methods such as the Homotopy perturbation, Adomian decomposition and Runge-Kutta fehlberg fourth-fifth order methods has been presented in the current paper. These methods have been applied in solving the system of the second order decomposition of ozone in aqueous solutions. The obtained results indicate these methods are appropriate to solve the equations whereas applying OHAM is more simpler with the same accuracy in comparison to other methods. [ABSTRACT FROM AUTHOR]

In this paper, optimal homotopy asymptotic method (OHAM) and multistage optimal homotopy asymptotic (MOHAM) method are applied to find an approximate solution to Abel's integral equation, that is in fact a weakly singular Volterra integral equation. To illustrate these approaches one example is presented. The results confirm the efficiency and ability of these methods to such equations. The results will be compared with the exact solution to find out that which method of these two is more accurate. [ABSTRACT FROM AUTHOR]

This paper attempts to carry out a study on a specific type of time-fractional differential equation called Benjamin-Bona-Mahony- Burger (BBM-Burger). This equation describes the mathematical model of unidirectional transmission of low-amplitude long waves through frequencydependent dispersive media. To go ahead the research, optimal homotopy asymptotic method (OHAM) and its new version (NOHAM) are applied to find analytic approximations to the BBM-Burger equation using the symbolic Maple package. Moreover, convergence of the both methods are addressed. The approximate results of the proposed methods are compared with the exact solution of BBM-Burger equation. What we learn from the results of applying OHAM and NOHAM on the BBM-Burger equation, is the high satisfactory accuracy. However, NOHAM produces an approximate solution with lower computational cost, than OHAM. [ABSTRACT FROM AUTHOR]

The effects of nanoparticle diameter on the magnetohydrodynamic flow and heat transfer of TiO2-H2O nanofluid over an exponentially stretching sheet are studied in this paper. It is assumed that the effective viscosity of TiO2-H2O nanofluid is a function of nanofluid concentration and nanoparticle diameter by use of new accurate correlation. Therefore, the flow and heat characteristics of TiO2-H2O nanofluid near a surface can be found under the effects of nanoparticle diameter for the first time. For this purpose, the governing partial differential equations are transformed to the nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved analytically using Optimal Homotopy Asymptotic Method (OHAM) which is most applicable in the analysis of nonlinear problems. The effects of nanoparticle diameter, nanofluid concentration, and magnetic field on the flow and heat transfer of nanofluid are investigated in detail. The results show that the reduced skin friction is a descending function of nanoparticle diameter. The reduced Nusselt number is a complicated function of magnetic field, nanofluid concentration, and nanoparticle diameter. It can be found that for the specific values of parameters, the curves of reduced Nusselt number with respect to the parameters such as magnetic field and nanofluid concentration have peaks where the maximum of heat transfer occurs. [ABSTRACT FROM AUTHOR]

Adomian decomposition method and optimal homotopy asymptotic method are successfully applied to find approximate solutions of a two moving boundaries problem governed with fractional time derivative in Caputo sense. Both approximate solutions are compared with the existing exact solution and numerical results are depicted through graphs and table. It is found that both techniques perform extremely well in terms of simplicity and accuracy. A brief study of dependence of moving boundaries on different parameters is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we implement the optimal homotopy asymptotic method to find the approximate solutions of the Poisson–Boltzmann equation. We also use the results of the conjugate gradient method for comparison with those of the optimal homotopy asymptotic method. Our study reveals that the optimal homotopy asymptotic method gives more effective results than conjugate gradient algorithms for the considered problems. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of non-Newtonian fluid of second grade. This model assumes that the flow and heat transfer in MHD viscoelastic fluid is subject to convective boundary conditions in the presence of electromagnetic field and nonuniform source/sink. The flow is considered over a porous sheet. The governing partial differential equations are converted as ordinary differential equations using suitable similarity transformations. The resulting coupled of nonlinear differential equations are successfully solved by means of Optimal Homotopy Asymptotic Method (OHAM). The effects of different physical parameters such as: the second-grade viscoelastic parameter, thermal radiation parameter or Eckert number are analyzed. Several closed form analytical approximate solutions for dimensionless stream function and temperature are presented for some particular cases. Our procedure is based upon an original construction of the solutions using a moderate number of the convergence-control parameters. These parameters lead to very high precision, comparing our approximate solutions with numerical solutions. Let us note that every nonlinear differential equation is reduced to two linear differential equations. The values of the convergence-control parameters are determined using rigorous mathematical procedures. OHAM is an iterative approach which rapidly converges after only one approximation, is effective, explicit, simple and easy to apply. These remarks are in fact the true power of our procedure to solving nonlinear problems without the presence of small or large parameters in the governing equations or boundary/initial conditions. [ABSTRACT FROM AUTHOR]

Nanoparticles are generally used to scatter and absorb solar radiations in nanofluid-based direct solar receivers to efficiently transport and store the heat. However, solar energy absorption in nanofluid can be enhanced by using differential materials and tuning nanofluid parameter. In this regard, theoretical investigations of unsteady homogeneous Hiemenz flow of an incompressible nanofluid having copper and silver nanoparticles over a porous wedge is carried out by using optimal homotopy asymptotic method (OHAM). Hence, a semi-analytical solver is applied to the transformed system to study the significance of magnetic field along with Prandtl number. In this work, impacts of conductive radiations, heat sink/source, unsteadiness, and flow parameters have been investigated for velocity and temperature profiles of copper and silver nanoparticles-based nanofluid. The effects of magnetic strength, volume fraction of nanoparticles, thermal conductivity, and flow parameters have also been studied on the considered nanofluids.

This paper proceeds from the perspective that most strongly nonlinear oscillators of fractional-order do not enjoy exact analytical solutions. Undoubtedly, this is a good enough reason to employ one of the major recent approximate methods, namely an Optimal Homotopy Asymptotic Method (OHAM), to offer approximate analytic solutions for two strongly fractional-order nonlinear benchmark oscillatory problems, namely: the fractional-order Duffing-relativistic oscillator and the fractional-order stretched elastic wire oscillator (with a mass attached to its midpoint). In this work, a further modification has been proposed for such method and then carried out through establishing an optimal auxiliary linear operator, an auxiliary function, and an auxiliary control parameter. In view of the two aforesaid applications, it has been demonstrated that the OHAM is a reliable approach for controlling the convergence of approximate solutions and, hence, it is an effective tool for dealing with such problems. This assertion is completely confirmed by performing several graphical comparisons between the OHAM and the Homotopy Analysis Method (HAM).

Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

In this research, the analytical methods of the differential transform method (DTM), homotopy asymptotic method (HAM), optimal homotopy asymptotic method (OHAM), Adomian decomposition method (ADM), variation iteration method (VIM) and reproducing kernel Hilbert space method (RKHSM), and the numerical method of the finite difference method (FDM) for (analytical-numerical) simulation of 2D viscous flow along expanding/contracting channels with permeable borders are carried out. The solutions for analytical method are obtained in series form (and the series are convergent), while for the numerical method the solution is obtained taking into account approximation techniques of second-order accuracy. The OHAM and HAM provide an appropriate method for controlling the convergence of the discretization series and adjusting convergence domains, despite having a problem for large sizes of obtained results in series form; for instance, the size of the series solution for the DTM is very small for the same order of accuracy. It is hard to judge which method is the best and all of them have their advantages and disadvantages. For instance, applying the DTM to BVPs is difficult; however, solving BVPs with the HAM, OHAM and VIM is simple and straightforward. The extracted solutions, in comparison with the computational solutions (shooting procedure combined with a Runge–Kutta fourth-order scheme, finite difference method), demonstrate remarkable accuracy. Finally, CPU time, average error and residual error for different cases are presented in tables and figures.

In this article, generalised Kudryashov technique has been implemented to construct new soliton solutions of modified Benjamin–Bona–Mahony (mBBM) equation. Also, the optimal homotopy asymptotic method (OHAM) has been employed to estimate the numerical solution. The solutions thus acquired by the above methods are illustrated graphically. The techniques considered here are efficacious, plausible and can be employed in mathematical physics to compute new exact and numerical solutions of NPDEs. [ABSTRACT FROM AUTHOR]

In this article, we employed Homotopy Perturbation Method (HPM) and Optimal Homotopy Asymptotic Method (OHAM) to investigate the semi analytical solution of thirteenth order boundary value problems. These analytical outcomes have been achieved in phrase of convergent series with simply computable constituents. Comparing the outcomes with exact solution, Variational Iterative Method (VIM) and Differential Transformative Method (DTM), excellent agreement has been found. It is observed that HPM and OHAM provide better solution than VIM and DTM which demonstrates the effectiveness, potentiality and validity of the proposed methods in reality and the acquired results are of top-level precision. [ABSTRACT FROM AUTHOR]

Applying the optimal homotopy asymptotic method (OHAM) to study three nonlinear problems, plane Couette flow, plane Poiseuille flow and plane Couette-Poiseuille flow, of the Oldroyd 6-constant fluid. Firstly, the governing equation and boundary condition of plane Couette flow, plane Poiseuille flow and plane Couette-Poiseuille flow in the Oldroyd 6-constant fluid were introduced respectively. Then applying the optimal homotopy asymptotic method was used to solve the problem, and carrying out some simulations. Finally, the effect of the slip parameter on the velocity profile was discussed based on the simulations. [ABSTRACT FROM AUTHOR]

This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solutions of temperature distribution in the domain 0 ≤x≤s(t) and interface’s tracking or location. The results thus obtained are compared with existing exact solutions for the case of the integer order derivative at some particular values of the governing parameters. The dependency of movement of the interface on certain parameters is also studied.

In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs) in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4) and Optimal Homotopy Asymptotic Method (OHAM-1). The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.

The nonlinear stability and the existence of the periodic solutions for an optimal control problem on the Schrödinger Lie group are discussed. The analytic solutions via optimal homotopy asymptotic method of the dynamics and numerical simulations are presented, too.

In this paper the thin film flow of an Oldroyd 6-constant fluid on a vertically moving belt is investigated. The basic equation of a non-Newtonian fluid in a container with a wide moving belt which passes through the container moving vertically upward with constant velocity, is reduced to an ordinary nonlinear differential equation. This equation is solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM). The solutions take into account the behavior of Newtonian and non-Newtonian fluids. Our procedure intended for solving nonlinear problems does not need small parameters in the equation and provides a convenient way to control the convergence of the approximate solutions.

In this article, optimal homotopy asymptotic method is presented to solve linear and nonlinear first-order conformable fractional differential equations that, is named conformable fractional optimal homotopy asymptotic method. So conformable fractional relaxation-oscillation and Riccati differential equations as a linear and nonlinear fractional differential equations, are solved by the proposed approach, respectively. The results obtained demonstrate the efficiency of the declared method for fractional equations. [ABSTRACT FROM AUTHOR]

Fractional differential equations are often seeming perplexing to solve. Therefore, finding comprehensive methods for solving them sounds of high importance. In this article, optimal homotopy asymptotic method is presented to solve specific second-order conformable fractional differential equations that is named conformable fractional optimal homotopy asymp-totic method. The results obtained demonstrate the efficiency of the declared method for fractional differential equations. Some numerical examples are presented to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]