On Double Shehu Transform and Its Properties with Applications
Main Article Content
Abstract
In the current paper, we have generalized the concept of one dimensional Shehu transform into two dimensional Shehu transform namely, double Shehu transform (DHT). Further, we have established some main properties and theorems related to the (DHT). To show the efficiency, high accuracy and applicability of the proposed transform, we have implemented the new transform to solve integral equations and partial differential equations.
Article Details
References
- R. N. Bracewell, The Fourier Transform and Its Applications (3rd ed.), McGraw-Hill, New York, (1986).
- D. V. Widder, The Laplace transform, Princeton University Press, Princeton, (1946).
- H. Eltayeb, A. Kilic ¸man, A note on double Laplace transform and telegraphic equations, Abstr. Appl. Anal. 2013 (2013), Article ID 932578.
- G. K. Watugala, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. J. Math. Educ. Sci. Technol. 24 (1993), 35-43.
- F. B. M. Belgacem, A. A. Karaballi, Sumudu transform fundamental properties investigations and applications, J. Appl. Math. Stoch. Anal. 2006 (2006), Article ID 91083.
- M. A. Asiru, Sumudu transform and the solution of integral equations of convolution type, Int. J. Math. Educ. Sci. Technol. 32 (2001), 906-910.
- S. K. Q. Al-Omari, On the application of natural transforms, Int. J. Pure Appl. Math. 85 (2013), 729-744.
- T. M. Elzaki, The new integral transform ”Elzaki transform”, Glob. J. Pure Appl. Math. 7(1) (2011), 57-64.
- P. K. G. Bhadane, V.H. Pradhan and S. V. Desale, Elzaki transform solution of one dimensional groundwater recharge through spreading, Int. J. Eng. Res. Appl.3 (6) (2013), 1607-1610.
- L. Debnath and D. Bhatta, Integral Transforms and Their Applications, CRC Press, Taylor Francis Group, Boca Raton, Fla, USA, 3rd edition, (2015).
- S. Maitama and W. Zhao, New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations, Int. J. Anal. Appl. 17 (2) (2019), 167-190.
- A. Khalouta and A. Kade, A New Method to Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, Appl. Appl. Math. 14 (2) (2019), 926-941.
- Aggarwal, Gupta, A.R and S., Sharma, N. A New Application of Shehu Transform for Handling Volterra Integral Equations of First Kind, Int. J. Res. Advent Technol. 7 (4) (2019), 438-445.
- A. Bokhari, D. Baleanu, and R. Belgacem. Application of Shehu transform to Atangana-Baleanu derivatives. J. Math. Computer Sci. 20 (2019), 101-107.
- R. Belgacem, D. Baleanu, and A. Bokhari , Shehu Transform and Applications to Caputo-Fractional Differential Equations. Int. J. Anal. Appl. 17 (6) (2019), 917-927.
- Dhunde, Ranjit R. and Waghmare, G.L. . Solving partial integro-differential equations using double Laplace transform method, Amer. J. Comput. Appl. Math. 5 (1) (2015), 7-10.
- Eltayeb, Hassan and Kilicman, Adem, On double Sumudu transform and double Laplace transform, Malaysian J. Math. Sci. 4 (1) (2010), 17-30.
- H. Eltayeb, A. Kili ¸cman, A note on the Sumudu transforms and differential equations, Appl. Math. Sci. 4 (22) (2010), 1089-1098.
- G. K. Watugala, The Sumudu transform for functions of two variables, Math. Eng. Ind. 8 (2002), 293-302.
- A. Kili ¸cman, H. Eltayeb, A note on integral transforms and partial differential equations, Appl. Math. Sci. 4 (2010), 109-118.
- Wazwaz, Abdul Majid . Partial Differential Equations and Solitary Waves Theory, Higher Education Press Beijing and Springer-Verlag, Berlin Heidelberg (2009).
- G. L. Lamb Jr, Introductory Applications of Partial Differential Equations with Emphasis on Wave Propagation and Diffusion, John Wiley & Sons, New York, NY, USA, (1995).