On numerical approximation of Atangana-Baleanu-Caputo fractional integro-differential equations under uncertainty in Hilbert Space

Many dynamic systems can be modeled by fractional differential equations in which some external parameters occur under uncertainty. Although these increase the complexity, they present more acceptable solutions. With aid of Atangana-Baleanu-Caputo (ABC) operator, an advanced numerical-analysis approach is considered and applied this work to deal with different classes fuzzy integrodifferential order fitted uncertain constraints conditions. The derivative ABC adopted generalized H-differentiability (g-HD) framework, uses Mittag-Leffler function as a nonlocal kernel better describe timescale models. Towards end, applications reproducing algorithm are extended solve linear nonlinear Volterra-Fredholm equations. Based on characterization theorem, preconditions established Lipschitz condition characterize solution coupled equivalent system crisp Parametric solutions interval provided terms rapidly convergent series Sobolev spaces. Several examples models implemented light g-HD demonstrate feasibility efficiency designed algorithm. Numerical graphical representations both classical Caputo derivatives presented show effect parametric posed achieved results reveal that proposed method systematic suitable for dealing problems arising physics, technology, engineering derivative.