?-Laplacian operator Arzèla Ascoli theorem Bäcklund transformation Caputo fractional derivative Clairin’s method Hilbert space Korteweg-de Vries equation Legendre wavelets Miura transformation Nagumo condition on the real line Navier–Stokes equations SIRS epidemic model Schauder’s fixed point theory Sumudu decomposition method a priori estimates asymptotic stability collocation method coupled nonlinear systems dichotomy difference equations differential equations discrete Lyapunov equation dissipation divided-difference equations dynamical system effective existence criteria exponential dichotomy exponential stability first order periodic systems fixed point theory