Fractional differential equations of variable order: existence results, numerical method and asymptotic stability conditionsGuo-Cheng Wu; Chuan-Yun Gu; Lan-Lan Huang; Dumitru Baleanu;
New variable-order fractional differential equations are proposed and numerical solutions are given in this paper. Firstly, a new way is introduced to define variable--order functions. The initial conditions are varied on different intervals and the fractional differential equations hold short memory effects or short-term interactions. Existence results are provided by Banach fixed point theorem successively over different intervals. Finally, predictor corrector method is improved and numerical examples are illustrated accordingly.
Vol. 23 (2022), No. 1, pp. 485-493