Limits...
New operational matrices for solving fractional differential equations on the half-line.

Bhrawy AH, Taha TM, Alzahrani EO, Baleanu D, Alzahrani AA - PLoS ONE (2015)

Bottom Line: We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods.Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms.We demonstrate the high accuracy and the efficiency of the proposed techniques.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt.

ABSTRACT
In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

No MeSH data available.


Comparing the exact solution and approximate solutions at N = 4, 6, where α = 0,  and γ = 0.1, for problem Eq (74).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4440753&req=5

pone.0126620.g001: Comparing the exact solution and approximate solutions at N = 4, 6, where α = 0, and γ = 0.1, for problem Eq (74).

Mentions: The solution of this problem is obtained by applying the technique described in Section 6.2 based on the FGLOM of fractional integration. The maximum absolute error for and various choices of N and α are shown in Table 4. Moreover, the approximate solution obtained by the proposed method for and two choices of N is shown in Fig 1 to make it easier to compare with the analytic solution. From this figure, we see the coherence of the exact and approximate solutions.


New operational matrices for solving fractional differential equations on the half-line.

Bhrawy AH, Taha TM, Alzahrani EO, Baleanu D, Alzahrani AA - PLoS ONE (2015)

Comparing the exact solution and approximate solutions at N = 4, 6, where α = 0,  and γ = 0.1, for problem Eq (74).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4440753&req=5

pone.0126620.g001: Comparing the exact solution and approximate solutions at N = 4, 6, where α = 0, and γ = 0.1, for problem Eq (74).
Mentions: The solution of this problem is obtained by applying the technique described in Section 6.2 based on the FGLOM of fractional integration. The maximum absolute error for and various choices of N and α are shown in Table 4. Moreover, the approximate solution obtained by the proposed method for and two choices of N is shown in Fig 1 to make it easier to compare with the analytic solution. From this figure, we see the coherence of the exact and approximate solutions.

Bottom Line: We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods.Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms.We demonstrate the high accuracy and the efficiency of the proposed techniques.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt.

ABSTRACT
In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

No MeSH data available.