Simple equations method (SEsM) and nonlinear PDEs with fractional derivatives
Nikolay K. Vitanov
Abstract
We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear differential equations. The focus of the discussion is on the application of the methodology to nonlinear PDEs with two kinds of fractional derivatives. We show that SEsM is applicable to nonlinear PDEs containing fractional derivatives. We show that several much used methods for obtaining exact solutions of nonlinear fractional differential equations are specific cases of SEsM.
Topics & Concepts
Nonlinear systemSimple (philosophy)Fractional calculusApplied mathematicsMathematicsFocus (optics)Partial differential equationDifferential equationNumerical partial differential equationsMathematical analysisPhysicsEpistemologyQuantum mechanicsPhilosophyOpticsNonlinear Waves and SolitonsFractional Differential Equations SolutionsNumerical methods for differential equations