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Full-Text Articles in Numerical Analysis and Computation
Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros
Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros
Mathematical Modelling and Numerical Simulation with Applications
This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and …
(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 …
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 …
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.
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.
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.