Nonlinear Inverse Problems for Equations with Dzhrbashyan–Nersesyan Derivatives

The unique solvability in the sense of classical solutions for nonlinear inverse problems to differential equations, solved oldest Dzhrbashyan–Nersesyan fractional derivative, is studied. linear part equation contains a bounded operator, continuous operator that depends on lower-order derivatives, and an unknown element. problem given by equation, special initial value conditions lower overdetermination condition, which defined operator. Applying fixed-point method contraction mapping theorem existence local solution proved under condition Lipschitz continuity mapping. Analogous nonlocal results were obtained case nonlocally equation. arbitrary Banach spaces used research with time-dependent coefficients at time-fractional derivatives integro-differential equations linearized system dynamics Kelvin–Voigt viscoelastic media.