Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order
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...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-06-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2017-0070 |
| _version_ | 1818580815984984064 |
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| author | Magesh N. Saravanan A. |
| author_facet | Magesh N. Saravanan A. |
| author_sort | Magesh N. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T07:23:36Z |
| format | Article |
| id | doaj.art-3fe6b0d047664802b365e17ab14a3024 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-16T07:23:36Z |
| publishDate | 2018-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-3fe6b0d047664802b365e17ab14a30242022-12-21T22:39:35ZengDe GruyterNonlinear Engineering2192-80102192-80292018-06-017212713510.1515/nleng-2017-0070Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer OrderMagesh N.0Saravanan A.1P. G. and Research Department of Mathematics, Govt Arts College for Men, Krishnagiri, 635001, IndiaDepartment of Mathematics, Sona College of Technology, Salem, 636 005, IndiaSystematic 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.https://doi.org/10.1515/nleng-2017-0070caputo fractional derivativefractional rlc circuitgeneralized differential transform methodlaplace transform methodseries solution34a0847n7001-08 |
| spellingShingle | Magesh N. Saravanan A. Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order Nonlinear Engineering caputo fractional derivative fractional rlc circuit generalized differential transform method laplace transform method series solution 34a08 47n70 01-08 |
| title | Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order |
| title_full | Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order |
| title_fullStr | Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order |
| title_full_unstemmed | Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order |
| title_short | Generalized Differential Transform Method for Solving RLC Electric Circuit of Non-Integer Order |
| title_sort | generalized differential transform method for solving rlc electric circuit of non integer order |
| topic | caputo fractional derivative fractional rlc circuit generalized differential transform method laplace transform method series solution 34a08 47n70 01-08 |
| url | https://doi.org/10.1515/nleng-2017-0070 |
| work_keys_str_mv | AT mageshn generalizeddifferentialtransformmethodforsolvingrlcelectriccircuitofnonintegerorder AT saravanana generalizeddifferentialtransformmethodforsolvingrlcelectriccircuitofnonintegerorder |