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This paper presents an efficient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the efficiency of the method with different coefficients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.
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참고문헌 (22)
참고문헌 신청
S. Abbasbandy / 2015 / Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation / Appl. Math. Comput 266:31~40
R. L. Bagley / 1983 / Fractional calculus: a different approach to the analysis of viscoelastically damped structures / AIAA J 21(5):741~748
D. Elliott / 1993 / An asymptotic analysis of two algorithms for certain Hadamard finite part integrals / IMA J. Numer. Anal 13(3):445~462
S. Kazem / 2013 / An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations / Appl. Math. Modell 37(3):1126~1136
S. Kazem / 2013 / Exact solution of some linear fractional differential equations by Laplace trans-form / Int. J. Nonlinear Sci 16(1):3~11
R. L. Bagley / 1983 / Fractional calculus: a different approach to the analysis of viscoelastically damped structures / AIAA J 21(5):741~748
D. Elliott / 1993 / An asymptotic analysis of two algorithms for certain Hadamard finite part integrals / IMA J. Numer. Anal 13(3):445~462
S. Kazem / 2013 / An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations / Appl. Math. Modell 37(3):1126~1136
S. Kazem / 2013 / Exact solution of some linear fractional differential equations by Laplace trans-form / Int. J. Nonlinear Sci 16(1):3~11
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