In this paper we have studied the combination of Elzaki and Laplace transforms to produce a degenerative new double integral transform, transform called Elzaki-Laplace (ELT), then applied it some partial differential equations find its exact solution.

We derive and discuss the analytical solution for the generalized time-fractional telegraph equation with the help of the Sumudu and Fourier transforms. In the process we use Green functions to derive the solution of the said differential equation.

For a wide class of solutions to multiplicatively advanced differential equations (MADEs), comprehensive set relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this relations, the current study forges systematic connection theory MADEs that special large subset general case, we introduce new family Schwartz wavelet MADE <math xmlns="http://www...

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...

Considering a Hamiltonian Dynamical System describing the motion of charged particle in a Tokamak or a Stellarator, we build a change of coordinates to reduce its dimension. This change of coordinates is in fact an intricate succession of mappings that are built using Hyperbolic Partial Differential Equations, Differential Geometry, Hamiltonian Dynamical System Theory and Symplectic Geometry, L...