An investigation of two integro-differential KP hierarchy equations to find out closed form solitons in mathematical physics

Solving two-dimensional fractional integro-differential equations by Legendre wavelets‎

‎In this paper‎, ‎we introduce the two-dimensional Legendre wavelets (2D-LWs)‎, ‎and develop them for solving a class of two-dimensional integro-differential equations (2D-IDEs) of fractional order‎. ‎We also investigate convergence of the method‎. ‎Finally‎, ‎we give some illustrative examples to demonstrate the validity and efficiency of the method.

Closed Form Solution of Qualitative Differential Equations

Numerical simulation, phase-space analysis, and analytic techniques are three methods used to solve quantitative differential equations . Most work in Qualitative Reasoning has dealt with analogs of the first two techniques, producing capabilities applicable to a wide range of systems . Although potentially of benefit, little has been done to provide closedform, analytic solution techniques for...

A New Technique of Reduce Differential Transform Method to Solve Local Fractional PDEs in Mathematical Physics

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...

Nonlinear Integro - Differential Equations

An improvement to the homotopy perturbation method for solving integro-differential equations