An approximation of the fractional integrals using quadratic interpolation

• Autorzy: Błaszczyk T. , Siedlecki J.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a numerical scheme to calculations of the left fractional integral. To calculate it we use the fractional Simpson’s rule (FSR). The FSR is derived by applying quadratic interpolation. We calculate errors generated by the method for particular functions and compare the obtained results with the fractional trapezoidal rule (FTR).

Słowa kluczowe

EN

fractional integrals; quadratic interpolation; Simpson’s rule

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 13--18
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Błaszczyk T.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Siedlecki J.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Leszczynski J.S., Blaszczyk T., Modeling the transition between stable and unstable operation while emptying a silo, Granular Matter 2011, 13, 429-438.
• [2] Magin R.L., Fractional Calculus in Bioengineering, Begell House Inc., Redding 2006.
• [3] Sumelka W., Blaszczyk T., Fractional continua for linear elasticity, Archives of Mechanics 2014, 66(3), 147-172.
• [4] Sun H.G., Zhang Y., Chen W., Reeves D.M., Use of a variable-index fractional-derivative model to capture transient dispersion in heterogeneous media, Journal of Contaminant Hydrology 2014, 157, 47–58
• [5] Agrawal O.P., Hasan M.M., Tangpong X.W., A numerical scheme for a class of parametric problem of fractional variational calculus, J. Comput. Nonlinear Dyn. 2012, 7, 021005-1-021005-6.
• [6] Baleanu D., Diethelm K., Scalas E., Trujillo J.J., Fractional Calculus Models and Numerical Methods, World Scientific, Singapore 2012.
• [7] Blaszczyk T., Ciesielski M., Klimek M., Leszczynski J., Numerical solution of fractional oscillator equation, Applied Mathematics and Computation 2011, 218, 2480-2488.
• [8] Blaszczyk T., Ciesielski M., Numerical solution of fractional Sturm-Liouville equation in integral form, Fract. Calc. Appl. Anal. 2014, 17, 307-320.
• [9] Fu Z.J., Chen W., Ling L., Method of approximate particular solutions for constant- and variable-order fractional diffusion models, Engineering Analysis with Boundary Elements 2014, DOI: 10.1016/j.enganabound.2014.09.003.
• [10] Novati P., Numerical approximation to the fractional derivative operator, Numerische Mathematik 2014, 127(3), 539-566.
• [11] Odibat Z., Approximations of fractional integrals and Caputo fractional derivatives, Applied Mathematics and Computation 2006, 178, 527-533.
• [12] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.