An inverse problem for a class of degenerate evolution multi-term equations with Gerasimov–Caputo derivatives

Issues of well-posedness of linear inverse problems for equations with several Gerasimov–Caputo fractional derivatives in Banach spaces are investigated. The inverse coefficient problem is considered for an equation solved with respect to the highest fractional derivative containing bounded operators at lower order derivatives. The criterion of well-posedness of such a problem is proved. A similar inverse problem for an equation with a degenerate operator at the highest derivative, assuming the relative 0-boundedness of a pair of operators at two higher derivatives, is reduced to two problems on subspaces for equations solved with respect to the highest derivative. The obtained well-posedness criteria allowed us to investigate one class of inverse problems for equations with polynomials from an elliptic differential operator with respect to spatial variables and with several Gerasimov–Caputo time derivatives.