scholarly journals Solving time-fractional chemical engineering equations by generalized differential transform method

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 157-164
Author(s):  
Ahmad Haghbin ◽  
Hossein Jafari ◽  
Pranay Goswami ◽  
Morganathan Ariyan
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Convergent Series ◽  
High Accuracy ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.

scholarly journals Solving time-fractional chemical engineering equations by generalized differential transform method

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 157-164
Author(s):  
Ahmad Haghbin ◽  
Hossein Jafari ◽  
Pranay Goswami ◽  
Morganathan Ariyan
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Convergent Series ◽  
High Accuracy ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Generalized Differential

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient.

Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order

2018 ◽  
Vol 7 (2) ◽  
pp. 127-135 ◽  
Author(s):  
N. Magesh ◽  
A. Saravanan
Keyword(s):  
Exact Solution ◽  
Initial Conditions ◽  
Electric Circuit ◽  
Convergent Series ◽  
Second Order ◽  
Differential Transform Method ◽  
Transform Method ◽  
Rlc Circuit ◽  
Differential Transform ◽  
Generalized Differential

AbstractSystematic construction of fractional ordinary differential equations [FODEs] has gained much attention nowadays research because dimensional homogeneity plays a major role in mathematical modeling. In order to keep up the dimension of the physical quantities, we need some auxiliary parameters. When we utilize auxiliary parameters, the FODE turns out to be more intricate. One of such kind of model is non-homogeneous fractional second order RLC circuit. To solve this kind of complicated FODEs, we need proficient modern analytical method. In this paper, we use two different methods, one is modern and the other is traditional, namely generalized differential transform Method (GDTM) and Laplace transform method (LTM) to obtain the analytical solution of non-homogeneous fractional second order RLC circuit. We present the solution in terms of convergent series. Though GDTM and LTM are capable to produce the exact solution of fractional RLC circuit, great strength of GDTM over LTM is that differential transform of initial conditions occupy the coefficients of first two terms in series solution so that we arrive exact solution with few iterations and also, it does not allow the noise terms while computing the coefficients. Due to this, GDTM takes less time to converge than LTM and it has been demonstrated. Furthermost, we discuss the characteristics of non-homogeneous fractional second order RLC circuit through numerical illustrations.

scholarly journals The GDTM-Padé Technique for the Nonlinear Lattice Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Junfeng Lu
Keyword(s):  
Exact Solutions ◽  
Padé Approximation ◽  
High Accuracy ◽  
Numerical Results ◽  
Differential Transform Method ◽  
Pade Approximation ◽  
Transform Method ◽  
Differential Transform ◽  
Nonlinear Lattice ◽  
Generalized Differential

The GDTM-Padé technique is a combination of the generalized differential transform method and the Padé approximation. We apply this technique to solve the two nonlinear lattice equations, which results in the high accuracy of the GDTM-Padé solutions. Numerical results are presented to show its efficiency by comparing the GDTM-Padé solutions, the solutions obtained by the generalized differential transform method, and the exact solutions.

scholarly journals NUMERICAL SOLUTION FOR TIME-FRACTIONAL MURRAY REACTION-DIFFUSION EQUATIONS VIA REDUCED DIFFERENTIAL TRANSFORM METHOD

2021 ◽  
Author(s):  
Muhammed Yiğider ◽  
Serkan Okur
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
Reaction Diffusion Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Reduced Differential Transform Method ◽  
Time Fractional Differential Equations

In this study, solutions of time-fractional differential equations that emerge from science and engineering have been investigated by employing reduced differential transform method. Initially, the definition of the derivatives with fractional order and their important features are given. Afterwards, by employing the Caputo derivative, reduced differential transform method has been introduced. Finally, the numerical solutions of the fractional order Murray equation have been obtained by utilizing reduced differential transform method and results have been compared through graphs and tables. Keywords: Time-fractional differential equations, Reduced differential transform methods, Murray equations, Caputo fractional derivative.

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