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Full-Text Articles in Physical Sciences and Mathematics
(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni
(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni
Applications and Applied Mathematics: An International Journal (AAM)
Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …
(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak
(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …
A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem
A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. …
Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan
Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan
Applications and Applied Mathematics: An International Journal (AAM)
The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.
A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak
A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
This paper introduces a generalization of the Fractional Optimal Control Problem (GFOCP). Proposed generalizations differ in terms of explaining the constraint involved in the dynamical system of the control problem. We assume the constraint as an arbitrary function of fractional derivatives and fractional integrals. By this assumption the restriction on constraint, to be of some prescribed function of fractional operators, is removed. Deduction of necessary optimality conditions followed by particular cases and examples has been provided. Additionally, we construct a solution scheme for the suggested class of (GFOCP)’s. The formulation of this scheme is done by implementing the Adomian decomposition …
On The Analytic Solution For The Steady Drainage Of Magnetohydrodynamic (Mhd) Sisko Fluid Film Down A Vertical Belt, A. M. Siddiqui, Hameed Ashraf, T. Haroon, A. Walait
On The Analytic Solution For The Steady Drainage Of Magnetohydrodynamic (Mhd) Sisko Fluid Film Down A Vertical Belt, A. M. Siddiqui, Hameed Ashraf, T. Haroon, A. Walait
Applications and Applied Mathematics: An International Journal (AAM)
This paper presents an analytic study for the steady drainage of magnetohydrodynamic (MHD) Sisko fluid film down a vertical belt. The fluid film is assumed to be electrically conducting in the presence of a uniform transverse magnetic field. An analytic solution for the resulting non linear ordinary differential equation is obtained using the Adomian decomposition method. The effects of various available parameters especially the Hartmann number are observed on the velocity profile, shear stress and vorticity vector to get a physical insight of the problem. Furthermore, the shear thinning and shear thickening characteristics of the Sisko fluid are discussed. The …
Analytic Solution For The Drainage Of Sisko Fluid Film Down A Vertical Belt, A. M. Siddiqui, Hameed Ashraf, T. Haroon, A. Walait
Analytic Solution For The Drainage Of Sisko Fluid Film Down A Vertical Belt, A. M. Siddiqui, Hameed Ashraf, T. Haroon, A. Walait
Applications and Applied Mathematics: An International Journal (AAM)
This paper deals with the drainage of Sisko fluid film down a vertical belt. It provides an approximate solution of the resulting non-linear and inhomogeneous ordinary differential equation using perturbation method (PM) and Adomian decomposition method (ADM). Comparison of the results obtained by both methods demonstrate that these series solutions are strictly identical but ADM is easy to compute and can be extended to any higher order. The important physical quantities like velocity profile, volume flow rate, average film velocity, shear stress, force exerted by the fluid film and vorticity vector are derived. The effects of fluid behaviour index, Stokes …
Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran
Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, system of fractional partial differential equation which has numerous applications in many fields of science is considered. Adomian decomposition method, a novel method is used to solve these type of equations. The solutions are derived in convergent series form which shows the effectiveness of the method for solving wide variety of fractional differential equations.
Approximating Solutions For Ginzburg – Landau Equation By Hpm And Adm, J. Biazar, M. Partovi, Z. Ayati
Approximating Solutions For Ginzburg – Landau Equation By Hpm And Adm, J. Biazar, M. Partovi, Z. Ayati
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an analytical approximation to the solution of Ginzburg-Landauis discussed. A Homotopy perturbation method introduced by He is employed to derive the analytic approximation solution and results compared with those of the Adomian decomposition method. Two examples are presented to show the capability of the methods. The results reveal that the methods are almost equally effective and promising.
Application Of Differential Transform Method To The Generalized Burgers–Huxley Equation, J. Biazar, F. Mohammadi
Application Of Differential Transform Method To The Generalized Burgers–Huxley Equation, J. Biazar, F. Mohammadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the differential transform method (DTM) will be applied to the generalized Burgers-Huxley equation, and some special cases of the equation, say, Huxley equation and Fitzhugh-Nagoma equation. The DTM produces an approximate solution for the equation, with few and easy computations. Numerical comparison between differential transform method, Adomian decomposition method and Variational iteration method for Burgers-Huxley, Huxley equation and Fitzhugh-Nagoma equation reveal that differential transform method is simple, accurate and efficient.
Comparison Differential Transformation Technique With Adomian Decomposition Method For Dispersive Long-Wave Equations In (2+1)-Dimensions, M. A. Mohamed
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we will introduce two methods to obtain the numerical solutions for the system of dispersive long-wave equations (DLWE) in (2+1)-dimensions. The first method is the differential transformation method (DTM) and the second method is Adomian decomposition method (ADM). Moreover, we will make comparison between the solutions obtained by the two methods. Consequently, the results of our system tell us the two methods can be alternative ways for solution of the linear and nonlinear higher-order initial value problems.