fractional-order‎ ‎pell hybrid‎ ‎functions for solving variable-order fractional differential equations and their application in chemistry

‎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. ‎