APPLICATIONS OF GENERALIZED SUMUDU TRANSFORM
Objective: To solve Cauchy Problem for the Wave Equation in One Dimensional Space using the generalized Sumudu transform.
Materials and Methods: We use the new integral transform called the Sumudu transform for the extension to a generalized space and we use the
method for extension followed by Zemanian.
Results and Conclusion: In this paper, I have established the application of generalized Sumudu transform. To illustrate the applications of
generalized Sumudu transform, I have applied it to solve the cauchy problem for the wave equation in one dimensional space where the initial
conditions are generalized functions.
type,Internat. J. Math.Ed.Sci.Tech.,32(2011),906–910.
 Asiru M.A.; Further Properties of the Sumudu Transform and its Applications, Internat.
 Asiru M. A.; Applications of the Sumudu Transform to Discrete Dynamic system. Internat.
J. Math. Ed. Sci. Tech.,34(6),(2003),944–949.
 Belgacem F.B.M.;Applications of the Sumudu Transformation Indefinite Periodic Parabolic
Equations,Proceedings of the International Conference on Nonlinear Problems and
Aerospace Applications,Budapest,Hungary, (2007),1–10.
 Belgacem F.B.M.;Introducing and Analyzing Deeper Sumudu Properties,Nonlinear Studies
 Belgacem F.B.M.,Karaballi A.A.,Kalla L.S.; nalytical investigations of the Sumudu transform
and applications to integral production equations, A,Math.Probl. Eng.,3(4),(2003),
 Belgacem F.B.M.,Karaballi A.A.,Kalla L.S.; Sumudu transform fundamental properties
investigations and applications, Journal of Applied Mathematics and Stochastic Analysis,
 Chindhe A.D.,Kiwne S.B.; Application of Sumudu Transform and Homotopy Perturbation
Method to Solve Nonlinear Differential Equations,MJIS,Chitkara University Publications,
 Chindhe A.D.,Kiwne S.B.;On The Generalized Natural Transform,Mathematical Journal of
 Deshna Loonker,Banerji PK.;Natural transform for distribution and Boehmian
spaces,Mathematics in Engineering,Science and Aerospace(MESA),Vol. 4, No.
 Deshna Loonker,Banerji PK.;On the solution of distributional Abel integral equation by
distributional Sumudu transform,Internat. J. Math. Math. Sci.,Article ID 480528,(2011),1-
 Deshna Loonker,Banerji PK.;Fractional Integrals and Derivatives for Sumudu transform
on distribution spaces,Appl. Appl. Math. Internat. J.,7 (1),(2012),188-200.
 Deshna Loonker,Banerji PK.;Hartley Transform for Integrable Boehmians,Int.Trans.
 Hassan Eltayeb ,Adem Kilicman, Brian Fisher ;New integral transform and associated
distributions,A Integral Transforms Special functions,21,(2010),367-379.
 Khan ZH,Khan WA.;N-transform properties and applications,NUST Journal of Engineering
 Pathak R.S.;Integral Transforms of Generalized Functions and their Applications,Gordon
and Breach Science Publishers,Australia, Canada, India,Japan,(1997).
 Sadikali Latif Shaikh;A Study of some Integral Transforms and their Operational Calculus,
 Sadikali Latif Shaikh ;Some Abelian Theorems for the Classical Sumudu Transform,
American International Journal of Research in Science, Technology, Engineering
 Shiraishi Risai;On the value of a distribution at a point and multiplicative products,J.
Sci.Hiroshima Univ. Ser. A-I 31,(1967),89-104.
 S.K.Q.Al-Omari;Generalized functions for double Sumudu transformation,International
Journal of Algebra, 6(3),(2011),139-146.
 S.K.Q.Al-Omari;On the Generalized Sumudu Transformation,journal of applied functional
 Thange T.G. and Chudhary M.S.;Some Integral Transform on Distribution Spaces,Ph. D.
Thesis, Shivaji University, Kolhapur,(2013).
 Watugala G. K.;Sumudu transform: a new integral transform to solve differential
equations and control engineering problems,Model Assisted Statistics and Applications,
 Watugala G. K.;Sumudu Transform A New Integral Transform to solve Differential
Equations and Control Engineering Problems,Mathematical Engineering in Industry,
 Watugala G. K.;The Sumudu transform for functions of two variables,Mathematical Engineering
 Weerakoon S.;Applications of Sumudu Transform to Partial Differential Equations,Int. J.
Math. Educ. Sci. Tech.,25(2),(1994),1277-283.
 Weerakoon S.;Complex Inversion formula for Sumudu Transform,Int. J. Math. Educ. Sci.
 Zemanian A.H.;Distribution Theory and Transform Analysis : An Introduction to Generalized
Functions with Applications,Mc-Graw Hill,New York,Republished by Dover Publication,
Inc., New York. 1965.
 Zemanian A.H.;Generalized Integral Transformations,Interscience Publishers, New
York,Republished by Dover Publications,Inc.,New York.1968.
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