Nonlinear inverse problems for a class of equations with Riemann–Liouville derivatives

The issues of local unique solvability in the sense of generalized and smooth solutions of nonlinear inverse problems for equations in Banach spaces with several fractional Riemann–Liouville derivatives and Riemann–Liouville integrals are investigated. The operator in the linear part is assumed to generate the analytic in the sector resolving family of operators of the corresponding linear equation, the unknown coefficients in the equation depend on time. The conditions of unique solvability of the inverse problem in Banach space are used in the study of a class of initial boundary value problems for a loaded fractional diffusion equation with several Riemann–Liouville derivatives and Riemann–Liouville integrals in time and unknown coefficients, with integral overdefinition conditions.