A novel double integral transform and its applications
Authors
Abdon Atangana
 Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of the Free State, , , 9300 Bloemfontein, South Africa.
Badr Saad T. Alkahtani
 Department of Mathematics, College of Science, King Saud University, P. O. Box 1142, Riyadh, 11989, Saudi Arabia.
Abstract
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.
Share and Cite
ISRP Style
Abdon Atangana, Badr Saad T. Alkahtani, A novel double integral transform and its applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 2, 424434
AMA Style
Atangana Abdon, Alkahtani Badr Saad T., A novel double integral transform and its applications. J. Nonlinear Sci. Appl. (2016); 9(2):424434
Chicago/Turabian Style
Atangana, Abdon, Alkahtani, Badr Saad T.. "A novel double integral transform and its applications." Journal of Nonlinear Sciences and Applications, 9, no. 2 (2016): 424434
Keywords
 Coincidence point
 new double integral transform
 Laplace transform
 second order partial differential equation.
MSC
References

[1]
E. Ahmed, A. M. A. ElSayed, A. E. M. ElMesiry, H. A. A. ElSaka, Numerical solution for the fractional replicator equation, Int. J. Mod. Phys. C, 16 (2005), 10171025.

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

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

[4]
A. Atangana, E. Alabaraoye, Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor onedimensional KellerSegel equations, Adv. Difference Equ., 2013 (2013), 14 pages.

[5]
A. Atangana, A. Secer, The TimeFractional CoupledKortewegdeVries Equations, Abstr. Appl. Anal., 2013 (2013), 8 pages.

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

[7]
C. M. Bender, K. S. Pinsky, L. M. Simmons, A new perturbative approach to nonlinear problems, J. Math. Phys., 30 (1989), 14471455.

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

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

[10]
P. Flajolet, X. Gourdon, P. Dumas, Mellin transforms and asymptotics: Harmonic sums, Theoret. Comput. Sci., 144 (1995), 358.

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

[12]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, NorthHolland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)

[13]
N. MaiDuy, R. I. Tanner , A collocation method based on onedimensional RBF interpolation scheme for solving PDEs, Int. J. Numer. Methods Heat Fluid Flow, 17 (2007), 165186.

[14]
A. Mehmood, A. Ali, Analytic homotopy solution of generalized threedimensional channel flow due to uniform stretching of the plate, Acta Mech. Sin., 23 (2007), 503510.

[15]
S. S. Motsa, P. Sibanda, S. Shateyi, A new spectralhomotopy analysis method for solving a nonlinear second order BVP, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 22932302.

[16]
A. H. Nayfeh, Order reduction of retarded nonlinear systemsthe method of multiple scales versus centermanifold reduction, Nonlinear Dynam., 51 (2008), 483500.

[17]
M. M. Rashidi, The modified differential transform method for solving MHD boundarylayer equations, Comput. Phys. Comm., 180 (2009), 22102217.

[18]
L. Schwartz, Transformation de Laplace des distributions, (in French), Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.], (1952), 196206.

[19]
Y. Tan, S. Abbasbandy, Homotopy analysis method for quadratic Riccati differential equation, Commun. Nonlinear Sci. Numer. Simul., 13 (2008), 539546.

[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, 16 (1935), 519524.

[21]
R. A. Van Gorder, K. Vajravelu, 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., 14 (2009), 40784089.

[22]
G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. J. Math. Edu. Sci. Tech., 24 (1993), 3543.

[23]
S. Weerakoon, The 'Sumudu transform' and the Laplace transform  Reply, Int. J. Math. Edu. Sci. Tech., 28 (1997), 159160.

[24]
H. Xu, Z. Lin, S. Liao, J. Wu, J. Majdalani, Homotopy based solutions of the NavierStokes equations for a porous channel with orthogonally moving walls, Phys. Fluids, 22 (2010), 118.