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

Nonlinear engineering: Modeling and application

article

N. Magesh¹  A. Saravanan² 

[1] P. G. and Research Department of Mathematics, Govt Arts College for Men;Department of Mathematics, Sona College of Technology

关键词: Caputo fractional derivative;    Fractional RLC circuit;    Generalized differential transform method;    Laplace transform method;    Series solution;   

DOI  :  10.1515/nleng-2017-0070

来源: De Gruyter

【 摘 要 】

Systematic 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.

【 授权许可】

Unknown