Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities

In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these is a locally uniformly convergent power series that can be chosen adequately to obtain family fractional and, in particular, main existing derivatives. Based on conditions for Laplace transform operators, some new results are obtained—for example, relationships between Riemann–Liouville and Caputo derivatives inverse operators. Later, employing representation product two functions, determine form calculating its derivative; result essential due connection derivative Lyapunov functions. addition, other developed, leading Lyapunov-like theorems direct method serves prove asymptotic stability sense FOB-stability concept introduced, which generalizes classical Mittag–Leffler wide class systems. Some inequalities established kernels, generalize others literature. Finally, via convex functions presented, whose importance lies avoiding calculation analysis dynamical illustrative examples given.