ON ONE NONLOCAL BOUNDARY-VALUE PROBLEM FOR A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH HILFER’S BI-ORDINAL DERIVATIVE

We consider a boundary-value problem with a nonlocal integral condition for a nonlinear fractional differential equation with a generalized (bi-ordinal) composite Hilfer’s derivative. The notion of a bi-ordinal Hilfer’s derivative is based on the interpolation concept with the use of Caputo and Riemann–Liouville derivatives of different orders. The existence of a solution and the uniqueness and stability of this problem are discussed. Keywords: nonlinear fractional-differential equations, bi-ordinal Hilfer’s derivative, boundary-value problem, nonlocal conditions, existence, uniqueness, stability.