Linear neutral partial differential equations: a semigroup approach

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Computational technique of linear partial differential equations by reduced differential transform ‎method

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physi...

Applied partial differential equations - a visual approach

Peter A. Markowich works in the area of partial differential equations and their applications in science and engineering. He holds a Chair in Applied Mathematics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge. He is also Professor at the University of Vienna and leader of a research group at the Johann Radon Institute for Computational and Applie...

Research Article Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the non...

Final Examination 18.303 Linear Partial Differential Equations