# zbMATH — the first resource for mathematics

Note on transport equation and fractional Sumudu transform. (English) Zbl 1232.44002
Summary: The Chebyshev polynomials to solve analytically the fractional neutron transport equation in one-dimensional plane geometry are used. The procedure is based on the expansion of the angular flux in terms of the Chebyshev polynomials. The obtained system of fractional linear differential equation is solved analytically by using fractional Sumudu transform.

##### MSC:
 44A10 Laplace transform 45K05 Integro-partial differential equations 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 33E12 Mittag-Leffler functions and generalizations 26A33 Fractional derivatives and integrals
Full Text:
##### References:
 [1] Watugala, G.K., Sumudu transforma new integral transform to solve differential equations and control engineering problems, Mathematical engineering in industry, 6, 4, 319-329, (1998) · Zbl 0916.44002 [2] Eltayeb, H.; Kılıçman, A., On some application of a new integral transform, International journal of mathematical analysis, 4, 3, 123-132, (2010) · Zbl 1207.34015 [3] Kılıçman, A.; Gadain, H.E., An application of double Laplace transform and double sumudu transform, Lobachevskii journal of mathematics, 30, 3, 214-223, (2009) · Zbl 1223.44002 [4] Belgacem, F.B.M., Boundary value problem with indefinite weight and applications, International journal of problems of nonlinear analysis in engineering systems, 10, 2, 51-58, (1999) [5] Eltayeb, H.; Kılıçman, A.; Fisher, B., A new integral transform and associated distributions, Integral transforms and special functions, 21, 5, 367-379, (2010) · Zbl 1191.35017 [6] Kılıçman, A.; Eltayeb, H., A note on integral transforms and partial differential equations, Applied mathematical sciences, 4, 3, 109-118, (2010) · Zbl 1194.35017 [7] Kılıçman, A.; Eltayeb, H., On the applications of Laplace and sumudu transforms, Journal of the franklin institute, 347, 5, 848-862, (2010) · Zbl 1286.35185 [8] A. Kılıçman, H. Eltayeb, P. Ravi Agarwal, On Sumudu transform and system of differential equations, Abstract and Applied Analysis, 2010, Article ID 598702, 11 pages. doi:10.1155/2010/598702. [9] Trzaska, Z., An efficient algorithm for partial expansion of the linear matrix pencil inverse, Journal of the franklin institute, 324, 465-477, (1987) · Zbl 0634.65028 [10] Kadem, A., Solving the one-dimensional neutron transport equation using Chebyshev polynomials and the sumudu transform, Analele universitatii din oradea fascicola matematič, 12, 153-171, (2005) · Zbl 1164.82331 [11] A. Kadem, A. Kılıçman, Note on the solution of transport equation by Tau method and Walsh functions, Abstract and Applied Analysis, 2010, Article ID 704168, 13 pages. doi:10.1155/2010/704168. [12] V.G. Gupta, S. Bhavna, A. Kılıçman, A note on fractional Sumudu transform, Journal of Applied Mathematics, 2010, Article ID 154189. doi:10.1155/2010/154189. · Zbl 1202.26014 [13] Kılıçman, A.; Gupta, V.G.; Sharma, B., On the solution of fractional Maxwell equations by sumudu transform, Journal of mathematics research, 2, 4, 147-151, (2010) · Zbl 1208.35163 [14] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., () [15] Luchko, Y.; Gorenflo, R., An operational method for solving fractional differential equation with the Caputo derivatives, Acta Mathematica vietnamica, 24, 2, 207-233, (1999) · Zbl 0931.44003 [16] Samko, G.; Kilbas, A.A.; Marichev, O.I., Fractional integrals and derivatives: theory and applications, (1993), Gordon and Breach Yverdon · Zbl 0818.26003 [17] Caputo, M., Linear models of dissipation whose $$Q$$ is almost frequency independent-II, Geophysical journal of the royal astronomical society, 13, 529-539, (1967) [18] Kiani-B., Arman; Fallahi, Kia; Pariz, Naser; Leung, Henry, A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter, Communications in nonlinear science and numerical simulation, 14, 863-879, (2009) · Zbl 1221.94049 [19] Miller, Kenneth S.; Ross, Bertram, An introduction to the fractional calculus and fractional differential equations, (1993), John Wiley & Sons · Zbl 0789.26002 [20] Podlubny, I., () [21] A. Loverro, Fractional calculus: history, definitions and applications for engineer, Department of Aerospace and Mechanical Engineering, University of Notre Dame, May 8 2004, pp. 870-884. [22] Tchuenche, M.; Mbare, N.S., An application of the double sumudu transform, Applied mathematical sciences, 1, 1-4, 31-39, (2007) · Zbl 1154.44001 [23] Chandrasekhar, S., Radiative transfer, (1960), Dover New York · Zbl 0037.43201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.