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Bulut, Hasan; Baskonus, Haci Mehmet; Belgacem, Fethi Bin Muhammad

The analytical solution of some fractional ordinary differential equations by the Sumudu transform method. (English) Zbl 1297.34005

Abstr. Appl. Anal. 2013, Article ID 203875, 6 p. (2013).
Summary: We introduce the basics of fractional calculus and applications of the Sumudu transform to fractional derivatives.

Cited in 36 Documents

MSC:

34A08 Fractional ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
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References:

[1] Watugala, G. K., Sumudu transform: a new integral transform to solve differential equations and control engineering problems, International Journal of Mathematical Education in Science and Technology, 24, 1, 35-43 (1993) · Zbl 0768.44003 · doi:10.1080/0020739930240105
[2] Watugala, G. K., Sumudu transform—a new integral transform to solve differential equations and control engineering problems, Mathematical Engineering in Industry, 6, 4, 319-329 (1998) · Zbl 0916.44002
[3] Watugala, G. K., The Sumudu transform for functions of two variables, Mathematical Engineering in Industry, 8, 4, 293-302 (2002) · Zbl 1025.44003
[4] Weerakoon, S., Application of Sumudu transform to partial differential equations, International Journal of Mathematical Education in Science and Technology, 25, 2, 277-283 (1994) · Zbl 0812.35004 · doi:10.1080/0020739940250214
[5] Weerakoon, S., Complex inversion formula for Sumudu transform, International Journal of Mathematical Education in Science and Technology, 29, 4, 618-621 (1998) · Zbl 1018.44004
[6] Deakin, M. A. B., The “Sumudu transform” and the Laplace transform, International Journal of Mathematical Education in Science and Technology, 28, 159 (1997) · Zbl 0885.44002
[7] Weerakoon, S., The “Sumudu transform” and the Laplace transform—reply, International Journal of Mathematical Education in Science and Technology, 28, 1, 160 (1997) · Zbl 0885.44003
[8] Asiru, M. A., Sumudu transform and the solution of integral equations of convolution type, International Journal of Mathematical Education in Science and Technology, 32, 6, 906-910 (2001) · Zbl 1008.45003 · doi:10.1080/002073901317147870
[9] Aşiru, M. A., Further properties of the Sumudu transform and its applications, International Journal of Mathematical Education in Science and Technology, 33, 3, 441-449 (2002) · Zbl 1013.44001 · doi:10.1080/002073902760047940
[10] Belgacem, F. B. M.; Karaballi, A. A.; Kalla, S. L., Analytical investigations of the Sumudu transform and applications to integral production equations, Mathematical Problems in Engineering, 3-4, 103-118 (2003) · Zbl 1068.44001 · doi:10.1155/S1024123X03207018
[11] Belgacem, F. B. M.; Karaballi, A., Sumudu transform fundamental properties investigations and applications, Journal of Applied Mathematics and Stochastic Analysis (2006) · Zbl 1115.44001 · doi:10.1155/JAMSA/2006/91083
[12] Belgacem, F. B. M., Introducing and analyzing deeper Sumudu properties Sumudu transform fundemantal properties investigations and applications, Nonlinear Studies Journal, 1, 31, 101-114 (2006)
[13] Belgacem, F. B. M., Applications of the Sumudu transform to indefinite periodic parabolic problems, Proceedings of the International Conference on Nonlinear Problems and Aerospace Applications (ICNPAA ’06)
[14] Hussain, M. G. M.; Belgacem, F. B. M., Transient solutions of Maxwell’s equations based on Sumudu transform, Progress in Electromagnetics Research, 74, 273-289 (2007)
[15] Belgacem, F. B. M., Sumudu applications to Maxwell’s equations, The Plan Index Enquiry and Retrieval System Online, 5, 355-360 (2009)
[16] Belgacem, F. B. M., Sumudu transform applications to Bessel functions and equations, Applied Mathematical Sciences, 4, 73-76, 3665-3686 (2010) · Zbl 1220.44001
[17] Katatbeh, Q. D.; Belgacem, F. B. M., Applications of the Sumudu transform to fractional differential equations, Nonlinear Studies, 18, 1, 99-112 (2011) · Zbl 1223.44001
[18] Salinas, S.; Jimenez, A.; Arteaga, F.; Rodriguez, J., Estudio analitico de la transformada de Sumudu y algunas aplicaciones a la teoria de control, Revista Ingeneria UC, 11, 3, 79-86 (2004)
[19] Rana, M. A.; Siddiqui, A. M.; Ghori, Q. K.; Qamar, R., Application of He’s homotopy perturbation method to Sumudu transform, International Journal of Nonlinear Sciences and Numerical Simulation, 8, 2, 185-190 (2007)
[20] Tamrabet, A.; Kadem, A., A combined Walsh function and Sumudu transform for solving the two-dimensional neutron transport equation, International Journal of Mathematical Analysis, 1, 9-12, 409-421 (2007) · Zbl 1130.45010
[21] Tchuenche, J. M.; Mbare, N. S., An application of the double Sumudu transform, Applied Mathematical Sciences, 1, 1-4, 31-39 (2007) · Zbl 1154.44001
[22] Zhang, J., Sumudu transform based coefficients calculation, Nonlinear Studies, 15, 4, 355-372 (2008) · Zbl 1177.65188
[23] Chaurasia, V. B. L.; Dubey, R. S.; Belgacem, F. B. M., Fractional radial diffusion equation analytical solution via Hankel and Sumudu transforms, International Journal of Mathematics in Engineering Science and Aerospace, 3, 2, 1-10 (2012) · Zbl 1247.26011
[24] Goswami, P.; Belgacem, F. B. M., Fractional differential equation solutions through a Sumudu rational, Nonlinear Studies, 19, 4, 591-598 (2012) · Zbl 1300.34016
[25] Belgacem, F. B. M., Introducing and analysing deeper Sumudu properties, Nonlinear Studies, 13, 1, 23-41 (2006) · Zbl 1102.44001
[26] Belgacem, F. B. M.; Silambarasan, R., Maxwell’s equations solutions by means of the natural transform, International Journal of Mathematics in Engineering, Science And Aeorospace, 3, 3, 313-323 (2012) · Zbl 1269.35042
[27] Alomari, S. K., An estimate of Sumudu transforms for Boehmians, Proceedings of the Conference on Mathematical problems in Engineering, Aerospace and Science
[28] Bulut, H.; Baskonus, H. M.; Tuluce, S., The solutions of partial differential equations with variable coefficients by sumudu transform method, AIP Proceeding, 1493, 91 (2012)
[29] Khan, H. Z.; Khan, W. A., N-transform-properties and applications, NUST Journal of Engineering Sciences, 1, 1, 127-133 (2008)
[30] Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Mathematical and Computer Modelling, 13, 7, 17-43 (1990) · Zbl 0713.65051 · doi:10.1016/0895-7177(90)90125-7
[31] Adomian, G.; Rach, R., Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations, Computers & Mathematics with Applications, 19, 12, 9-12 (1990) · Zbl 0702.35058 · doi:10.1016/0898-1221(90)90246-G
[32] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method. Solving Frontier Problems of Physics: The Decomposition Method, Fundamental Theories of Physics, 60, xiv+352 (1994), Boston, Mass, USA: Kluwer Academic Publishers, Boston, Mass, USA · Zbl 0802.65122
[33] Adomian, G., A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 135, 2, 501-544 (1988) · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[34] Deng, Z.-G.; Wu, G.-C., Approximate solution of fractional differential equations with uncertainty, Romanian Journal of Physics, 56, 7-8, 868-872 (2011)
[35] Abdou, M. A.; Soliman, A. A., Variational iteration method for solving Burger’s and coupled Burger’s equations, Journal of Computational and Applied Mathematics, 181, 2, 245-251 (2005) · Zbl 1072.65127 · doi:10.1016/j.cam.2004.11.032
[36] Odibat, Z. M.; Momani, S., Application of variational iteration method to nonlinear differential equations of fractional order, International Journal of Nonlinear Sciences and Numerical Simulation, 7, 1, 27-34 (2006) · Zbl 1401.65087
[37] He, J.-H.; Wu, X.-H., Variational iteration method: new development and applications, Computers & Mathematics with Applications, 54, 7-8, 881-894 (2007) · Zbl 1141.65372 · doi:10.1016/j.camwa.2006.12.083
[38] Sweilam, N. H., Fourth order integro-differential equations using variational iteration method, Computers & Mathematics with Applications, 54, 7-8, 1086-1091 (2007) · Zbl 1141.65399 · doi:10.1016/j.camwa.2006.12.055
[39] Abbasbandy, S., A new application of He’s variational iteration method for quadratic Riccati differential equation by using Adomian’s polynomials, Journal of Computational and Applied Mathematics, 207, 1, 59-63 (2007) · Zbl 1120.65083 · doi:10.1016/j.cam.2006.07.012
[40] Wazwaz, A.-M., The variational iteration method for exact solutions of Laplace equation, Physics Letters A, 363, 4, 260-262 (2007) · Zbl 1197.65204 · doi:10.1016/j.physleta.2006.11.014
[41] Asiru, M. A., Application of the sumudu transform to discrete dynamical systems, International Journal of Mathematical Education, Science and Technology, 34, 6, 944-949 (2003)
[42] Bulut, H.; Baskonus, H. M.; Tuluce, S., Homotopy perturbation sumudu transform method for heat equations, Mathematics in Engineering, Science and Aerospace, 4, 1, 49-60 (2013) · Zbl 1262.35005
[43] Jarad, F.; Taş, K., On Sumudu transform method in discrete fractional calculus, Abstract and Applied Analysis, 2012 (2012) · Zbl 1253.34014 · doi:10.1155/2012/270106
[44] Gupta, V. G.; Shrama, B.; Kiliçman, A., A note on fractional Sumudu transform, Journal of Applied Mathematics, 2010 (2010) · Zbl 1202.26014 · doi:10.1155/2010/154189
[45] Mittal, R. C.; Nigam, R., Solution of fractional integro-differential equations by adomian decomposition method, The International Journal of Applied Mathematics and Mechanics, 4, 2, 87-94 (2008)
[46] Podlubny, I., Fractional Differential Equations. Fractional Differential Equations, Mathematics in Science and Engineering, 198, xxiv+340 (1999), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0924.34008
[47] Caputo, M., Linear model of dissipation whose Q is almost frequency independent-II, Geophysical Journal of the Royal Astronomical Society, 13, 5, 529-539 (1967)
[48] Belgacem, F. B. M.; Silambarasan, R., The Sumudu transform analysis by infinite series, Proceedings of the AIP Proceeding
[49] Goswami, P.; Belgacem, F. B. M., Solving special fractional differential equations by the Sumudu transform, Proceedings of the AIP Proceeding
[50] Odibat, Z. M.; Momani, S., An algorithm for the numerical solution of differential equations of fractional order, Journal of Applied Mathematics and Informatics, 26, 1-2, 15-127
[51] Ford, N. J.; Simpson, A. C., The numerical solution of fractional differential equations: speed versus accuracy, Numerical Analysis Report, no. 385 (2003), A Report in Association with Chester College
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