On an application of Laplace transforms

Year 2017, Volume: 5 Issue: 2, 193 - 198, 30.03.2017

Murat Duz

Abstract

In this study, complex differential equations are solved using laplace transform. Firstly we seperate real and imaginer parts of equation. Thus from one unknown equation is obtained two unknown equation system. Later we obtain laplace transforms of real and imaginer parts of solutions using laplace transform. In the latest we obtain real and imaginer parts of solution using inverse laplace transform.

Keywords

Laplace transform, inverse Laplace transform, dirac delta function

References

• Yin, F. K., Han, W. Y.and Song, J. Q, “Modified Laplace decomposition method for Lane-Emden Type differential equations”, International Jaurnal of Applied Physics and Matematics, 3 (2): 98-102 (2013).
• Mohamed, M. A. and Torky, M. S., “Numerical solution of nonlinear system of parial differential equations by the Laplace decomposition method and the padeapproximation”, American Journal of Computational Mathematics,3 (3): 175-184 (2013).
• Yusufoglu, E., “Numerical Solution of duffing equation by the Laplace decomposition algorithm”, Applied Mathematics and Computation,177 (2): 572-580 (2006).
• Kazem, S.,”Exact Solution of Some Linear Fractional Differential Equations by Laplace Transform”, International Journal of Nonlinear Science, 16 (2013) No:1 pp. 3-11.
• Kexue, L., Jigen, P. ”Laplace transform and fractional differential equations”, Applied Mathematics Letters, 24 (2011) 2019–2023.
• Gupta, S., Kumar, D., Singh, J.”Numerical study for systems of fractional differential equations via Laplace transform ”, Journal of the Egyptian Mathematical Society, (2015) 23, 256–262.