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ENHANCED SEMI-ANALYTIC METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

  • JANG, BONGSOO (DEPARTMENT OF MATHEMATICAL SCIENCES, ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHONOLOGY(UNIST)) ;
  • KIM, HYUNJU (DEPARTMENT OF MATHEMATICS, NORTH GREENVILLE UNIVERSITY)
  • Received : 2019.09.21
  • Accepted : 2019.12.02
  • Published : 2019.12.25

Abstract

In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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