Generalized Gegenbauer-Humbert wavelets for solving fractional partial differential equations - Alkhalissi, Jumana H. S.; Emiroglu, Ibrahim; Bayram, Mustafa; Secer, Aydin; Tasci, Fatih (SPRINGER, 2023)
This article develops a method based on the generalized Gegenbauer-Humbert wavelets in concert with their operational matrices of fractional integration to deal with the fractional partial differential equations and find the approximate solutions of it. The goal is to show that the proposed method is appropriate for boundary and initial-boundary problems even though it is generalized form. The convergence of the method under study is investigated. The numerical results gained by the proposed method are considered and compared with other methods, to establish the effectiveness and accuracy.
Keywords: Fractional partial differential equations; The generalized Gegenbauer-Humbert; Operational matrix; CONVECTION-DIFFUSION EQUATIONS; BERNOULLI WAVELETS; NUMERICAL-SOLUTION; COLLOCATION METHOD; ORDER INTEGRATION; SCHEME; Computer Science; Engineering