Fibonacci wavelets-based numerical method for solving fractional order (1 + 1)-dimensional dispersive partial differential equation

A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method

“…A lot of mathematicians have also recently introduced several new techniques for solving differential equations, such as the Hermite wavelet technique [4], the Bäcklund transformation method [5], the Fibonacci wavelet scheme for solving hyperbolic PDE, dispersive PDE, the Rosenau-Hyman equation [6][7][8], the first integral method for MBBM equation [9], Hirota's bilinear method [10], Bernoulli wavelet scheme for nonlinear Murray equation [11], BBMB equations by Exp-Function method [12], (2+1) dimensional Sobolev equation via wavelet technique [13], the Haar wavelet method for the BBM equations [14], ultraspherical wavelet scheme for spectral solutions of Riccati equations [15], ultraspherical wavelet technique for solving 2nth-order boundary value problems [16], ultraspherical operational matrices of derivatives [17], clique polynomial and Adomian decomposition method for solving differential equations [18], and Laguerre wavelets scheme for solving delay differential equations [19], Bernoulli wavelet technique for solving biological models [20], explicit solution of atmospheresoil-land plant carbon cycle system [21], study on Kudryashov-Sinelshchikov dynamical equation [22], study on Caudrey-Dodd-Gibbon-Sawada-Kotera partial differential equation [23], structure of the analytic solutions for Schrödinger equation [24], solutions for Konopelchenko-Dubrovsky equation [25], solutions of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation [26], solutions of the Korteweg-de Vries-Zakharov-Kuznetsov equation [27].…”