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Articles 121 - 138 of 138
Full-Text Articles in Analysis
Exact Soliton Solutions For Second-Order Benjamin-Ono Equation, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz
Exact Soliton Solutions For Second-Order Benjamin-Ono Equation, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz
Applications and Applied Mathematics: An International Journal (AAM)
The homogeneous balance method is proposed for seeking the travelling wave solutions of the second-order Benjamin-Ono equation. Many exact traveling wave solutions of second-order Benjamin-Ono equation, which contain soliton like and periodic-like solutions are successfully obtained. This method is straightforward and concise, and it may also be applied to other nonlinear evolution equations.
Algorithms To Solve Singularly Perturbed Volterra Integral Equations, Marwan T. Alquran, Bilal Khair
Algorithms To Solve Singularly Perturbed Volterra Integral Equations, Marwan T. Alquran, Bilal Khair
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the Differential Transform Method (DTM) and Variational Iterative Method (VIM) to develop algorithms for solving singularly perturbed volterra integral equations (SPVIEs). The study outlines the significant features of the two methods. A comparison between the two methods for the solution of SPVIs is given for three examples. The results show that both methods are very efficient, convenient and applicable to a large class of problems.
Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf
Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf
Applications and Applied Mathematics: An International Journal (AAM)
The objective of this paper is to use Neural Networks for solving boundary value problems (BVPs) in Ordinary Differential Equations (ODEs). The Neural networks use the principle of Back propagation. Five examples are considered to show effectiveness of using the shooting techniques and neural network for solving the BVPs in ODEs. The convergence properties of the technique, which depend on the convergence of the integration technique and accuracy of the interpolation technique are considered.
Exact Travelling Wave Solutions Of The Coupled Klein-Gordon Equation By The Infinite Series Method, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz
Exact Travelling Wave Solutions Of The Coupled Klein-Gordon Equation By The Infinite Series Method, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we employ the infinite series method for travelling wave solutions of the coupled Klein-Gordon equations. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons and periodic solutions.
On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla
On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
The object of this paper is to give a generalization of Gauss hypergeometric function, and to investigate its basic properties. Further, we define some fractional integral operators and their inverses in terms of the Mellin transform. Several well known integral operators, including Saigo operators can be derived from the results established here.
Exact Solutions Of The Generalized- Zakharov (Gz) Equation By The Infinite Series Method, N. Taghizadeh, M. Mirzazadeh, F. Farahrooz
Exact Solutions Of The Generalized- Zakharov (Gz) Equation By The Infinite Series Method, N. Taghizadeh, M. Mirzazadeh, F. Farahrooz
Applications and Applied Mathematics: An International Journal (AAM)
The infinite series method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the direct algebraic method is used to construct new exact solutions of generalized- Zakharov equation.
Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal
Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.
Solutions Of Nonlinear Second Order Multi-Point Boundary Value Problems By Homotopy Perturbation Method, S. Das, Sunil Kumar, O. P. Singh
Solutions Of Nonlinear Second Order Multi-Point Boundary Value Problems By Homotopy Perturbation Method, S. Das, Sunil Kumar, O. P. Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present an algorithm for the numerical solution of the second order multi- point boundary value problem with suitable multi boundary conditions. The algorithm is based on the homotopy perturbation approach and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solutions that converge very rapidly in physical problems. Illustrative numerical examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multipoint boundary value problems.
Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari
Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari
Applications and Applied Mathematics: An International Journal (AAM)
This article presents the approximate analytical solutions of first order linear partial differential equations (PDEs) with fractional time- and space- derivatives. With the aid of initial values, the explicit solutions of the equations are solved making use of reliable algorithm like homotopy analysis method (HAM). The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described in Caputo sense. Numerical results show that the HAM is easy to implement and accurate when applied to space- time- fractional PDEs.
On The Eigenvalue And Inertia Problems For Descriptor Systems, Asadollah Aasaraai, Kameleh N. Pirbazari
On The Eigenvalue And Inertia Problems For Descriptor Systems, Asadollah Aasaraai, Kameleh N. Pirbazari
Applications and Applied Mathematics: An International Journal (AAM)
The present study is intended to demonstrate that for a descriptor system with matrix pencil there exists a matrix such that matrix and matrix pencil have the same positive and negative eigenvalues. It is also shown that matrix can be calculated as a contour integral. On the other hand, different representations for matrix are introduced.
An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta
An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta
Applications and Applied Mathematics: An International Journal (AAM)
In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.
Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla
Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.
Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia
Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia
Applications and Applied Mathematics: An International Journal (AAM)
A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.
An Efficient Technique For Solving Special Integral Equations, Jafar Biazar, Mostafa Eslami
An Efficient Technique For Solving Special Integral Equations, Jafar Biazar, Mostafa Eslami
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply a new technique for solving two-dimensional integral equations of mixed type. Comparisons are made between the homotopy perturbation method and the new technique. The results reveal that the new technique is effective and convenient.
Mehler-Fock Transformation Of Ultradistribution, Deshna Loonker, P. K. Banerji
Mehler-Fock Transformation Of Ultradistribution, Deshna Loonker, P. K. Banerji
Applications and Applied Mathematics: An International Journal (AAM)
This paper deals with the testing function space Z and its dual Z', which is known as ultradistrbution. Some theorems and properties are investigated for the Mehler-Fock transformation and its inverse for the ultradistribution.
Analytical Solution Of Time-Fractional Advection Dispersion Equation, Tariq O. Salim, Ahmad El-Kahlout
Analytical Solution Of Time-Fractional Advection Dispersion Equation, Tariq O. Salim, Ahmad El-Kahlout
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we get exact solution of the time-fractional advection-dispersion equation with reaction term, where the Caputo fractional derivative is considered of order α ϵ (0,2]. The solution is achieved by using a function transform, Fourier and Laplace transforms to get the formulas of the fundamental solution, which are expressed explicitly in terms of Fox’s H-function by making use of the relationship between Fourier and Mellin transforms. As special cases the exact solutions of time-fractional diffusion and wave equations are also obtained, and the solutions of the integer order equations are mentioned.
Certain Expansion Formulae Involving A Basic Analogue Of Fox’S H-Function, S. D. Purohit, R. K. Yadav, S. L. Kalla
Certain Expansion Formulae Involving A Basic Analogue Of Fox’S H-Function, S. D. Purohit, R. K. Yadav, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results.
A Complexification Of Rolle’S Theorem, J. P. Pemba, A. R. Davies, N. K. Muoneke
A Complexification Of Rolle’S Theorem, J. P. Pemba, A. R. Davies, N. K. Muoneke
Applications and Applied Mathematics: An International Journal (AAM)
A new version of the classical Rolle’s theorem is proved for any complex-valued differentiable function of the complex variable on an open connected convex subset of the complex field. The associated Mean-Value theorem follows naturally. A few explicit illustrative examples are provided in the closing section of the paper.