Exact solutions to conformable time-fractional Klein–Gordon equation with high-order nonlinearities
Li Tang
Abstract
In this paper, we solve the conformal time-fractional Klein–Gordon equation with high-order nonlinearities via the complete discrimination system for polynomial method, namely with the quadratic and cubic nonlinearities. Our results contain all the existing solutions, and some new exact solutions such as Jacobian elliptic function solutions, are also presented. Moreover, to ensure the existence of each solution, the concrete examples are given and the discussions of the influence of the fractional order are also presented.
Topics & Concepts
Conformable matrixKlein–Gordon equationOrder (exchange)MathematicsConformal mapQuadratic functionPolynomialQuadratic equationFunction (biology)Mathematical analysisApplied mathematicsJacobian matrix and determinantElliptic functionFractional calculusExact solutions in general relativityNonlinear systemPhysicsGeometryBiologyEvolutionary biologyFinanceEconomicsQuantum mechanicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsAdvanced Differential Equations and Dynamical Systems