On Approximate Solutions for Fractional Logistic Differential Equation
A new approximate formula of the fractional derivatives is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Specia...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2013/391901 |
| Summary: | A new approximate formula of the fractional derivatives is derived. The
proposed formula is based on the generalized Laguerre polynomials. Global approximations
to functions defined on a semi-infinite interval are constructed. The fractional derivatives
are presented in terms of Caputo sense. Special attention is given to study the convergence
analysis and estimate an error upper bound of the presented formula. The new spectral Laguerre
collocation method is presented for solving fractional Logistic differential equation (FLDE). The
properties of Laguerre polynomials approximation are used to reduce FLDE to solve a system
of algebraic equations which is solved using a suitable numerical method. Numerical results are
provided to confirm the theoretical results and the efficiency of the proposed method. |
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| ISSN: | 1024-123X 1563-5147 |