A novel double integral transform and its applications
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 424-434.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We introduce a new double integral equation and prove some related theorems. We then present some useful tools for the new integral operator, and use this operator to solve partial differential equations with singularities of a given type.
DOI : 10.22436/jnsa.009.02.08
Classification : 31A10, 31A25, 31B20
Keywords: Coincidence point, new double integral transform, Laplace transform, second order partial differential equation.

Atangana, Abdon 1 ; Alkahtani, Badr Saad T. 2

1 Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of the Free State, , , 9300 Bloemfontein, South Africa
2 Department of Mathematics, College of Science, King Saud University, P. O. Box 1142, Riyadh, 11989, Saudi Arabia
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Atangana, Abdon; Alkahtani, Badr Saad T. A novel double integral transform and its applications. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 2, p. 424-434. doi : 10.22436/jnsa.009.02.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.02.08/

[1] Ahmed, E.; El-Sayed, A. M. A.; El-Mesiry, A. E. M.; El-Saka, H. A. A. Numerical solution for the fractional replicator equation, Int. J. Mod. Phys. C, Volume 16 (2005), pp. 1017-1025

[2] Andrianov, I.; Manevitch, L. Asymptotology, Ideas, Methods, and Applications, Kluwer Academic Publishers, Dordrecht, 2002

[3] Atangana, A. A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third order differential Equation, Abstr. Appl. Anal., Volume 2013 (2013), pp. 1-10

[4] Atangana, A.; Alabaraoye, E. Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller-Segel equations, Adv. Difference Equ., Volume 2013 (2013), pp. 1-14

[5] Atangana, A.; Secer, A. The Time-Fractional Coupled-Korteweg-de-Vries Equations, Abstr. Appl. Anal., Volume 2013 (2013), pp. 1-8

[6] Awrejcewicz, J.; Krysko, V. A. Introduction to Asymptotic Methods, Chapman and Hall, CRC Press, Boca Raton, Chapman & Hall/CRC, Boca Raton, 2006

[7] Bender, C. M.; Pinsky, K. S.; Simmons, L. M. A new perturbative approach to nonlinear problems, J. Math. Phys., Volume 30 (1989), pp. 1447-1455

[8] Bracewell, R. N. The Fourier Transform and Its Applications , (3rd ed.), McGraw-Hill, New York, 1986

[9] Eltayeb, H.; Kılıçman, A. A Note on Double Laplace Transform and Telegraphic Equations, Abstr. Appl. Anal., Volume 2013 (2013), pp. 1-6

[10] Flajolet, P.; Gourdon, X.; Dumas, P. Mellin transforms and asymptotics: Harmonic sums, Theoret. Comput. Sci., Volume 144 (1995), pp. 3-58

[11] Galambos, J.; Simonelli, I. Products of random variables: applications to problems of physics and to arithmetical functions, Marcel Dekker, Inc., New York, 2004

[12] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J. Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, 2006

[13] Mai-Duy, N.; R. I. Tanner A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs, Int. J. Numer. Methods Heat Fluid Flow, Volume 17 (2007), pp. 165-186

[14] Mehmood, A.; Ali, A. Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate, Acta Mech. Sin., Volume 23 (2007), pp. 503-510

[15] Motsa, S. S.; Sibanda, P.; Shateyi, S. A new spectral-homotopy analysis method for solving a nonlinear second order BVP, Commun. Nonlinear Sci. Numer. Simul., Volume 15 (2010), pp. 2293-2302

[16] Nayfeh, A. H. Order reduction of retarded nonlinear systems-the method of multiple scales versus centermanifold reduction, Nonlinear Dynam., Volume 51 (2008), pp. 483-500

[17] Rashidi, M. M. The modified differential transform method for solving MHD boundary-layer equations, Comput. Phys. Comm., Volume 180 (2009), pp. 2210-2217

[18] Schwartz, L. Transformation de Laplace des distributions, (in French), Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] (1952), pp. 196-206

[19] Tan, Y.; Abbasbandy, S. Homotopy analysis method for quadratic Riccati differential equation, Commun. Nonlinear Sci. Numer. Simul., Volume 13 (2008), pp. 539-546

[20] C. V. Theis The relation between the lowering of the piezometric surface and the rate and duration of discharge of well using groundwater storage, Trans. Amer. Geophys. Union, Volume 16 (1935), pp. 519-524

[21] Gorder, R. A. Van; Vajravelu, K. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach, Commun. Nonlinear Sci. Numer. Simul., Volume 14 (2009), pp. 4078-4089

[22] Watugala, G. K. Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. J. Math. Edu. Sci. Tech., Volume 24 (1993), pp. 35-43

[23] Weerakoon, S. The 'Sumudu transform' and the Laplace transform - Reply, Int. J. Math. Edu. Sci. Tech., Volume 28 (1997), pp. 159-160

[24] Xu, H.; Lin, Z.; Liao, S.; Wu, J.; Majdalani, J. Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls, Phys. Fluids, Volume 22 (2010), pp. 1-18

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