Fractional-Order Pell Hybrid Functions for Solving Variable-Order Fractional Differential Equations and their Application in Chemistry

چکیده مقاله

Herein, we introduce a novel computational approach to find a solution of variable-order fractional differential equations (VO-FDE). The desired method is proposed by combining fractional-order Pell functions, the Ritz and collocation methods. First, we define a new set of hybrid functions named fractional-order Pell hybrid functions. Next, to approximate the solution of VO-FDEs, we obtain an extra pseudo-operational matrix of the Caputo variable-order derivative. Then, by using the Ritz method, the operational matrix approach, and the collocation method, the problem is transformed to a system of algebraic equations, which is solved by Newton’s iterative method. The error estimation of the proposed method is also examined. Finally, some examples (especially in chemistry) are presented to illustrate the effectiveness of this method. © 2025, University of Kashan. All right resevered.