Analytical solutions of generalized differential equations using quadratic-phase Fourier transform
Firdous A. Shah, Waseem Z. Lone, Kottakkaran Sooppy Nisar, Amany Salah Khalifa
Abstract
<abstract><p>The aim of this study is to obtain the analytical solutions of some prominent differential equations including the generalized Laplace, heat and wave equations by using the quadratic-phase Fourier transform. To facilitate the narrative, we formulate the preliminary results vis-a-vis the differentiation properties of the quadratic-phase Fourier transform. The obtained results are reinforced with illustrative examples.</p></abstract>
Topics & Concepts
Fourier transformLaplace transformMathematicsQuadratic equationMathematical analysisPhase (matter)PhysicsGeometryQuantum mechanicsFractional Differential Equations SolutionsMathematical Analysis and Transform MethodsImage and Signal Denoising Methods