Generalized Fourier-Laplace Transform and Differential Equations

Abstract

Integral transformations are very important tool for solving various problems in mathematics, physics and engineering. Fourier and Laplace transforms are powerful tools for image processing and signal processing. However we have combined these transforms to form Fourier-Laplace transform and tried to solve different types of problems. This paper gives the application of generalized Fourier-Laplace transform for solving some differential equations. Also we introduced new differential operator and its adjoint operator and solved the Differential equations using Fourier-Laplace transform.