QUASILINEAR EQUATIONS WITH RIEMANN - LIOUVILLE DERIVATIVES IN H¨OLDER TYPE SPACES (2025)
Выпуск:
Т. 10 № 1 (2025)
The issues of the unique solvability of a Cauchy type problem for a quasilinear equation in a Banach space with several minor fractional derivatives in the nonlinear part and with a linear operator generating an analytical resolving family of operators of a linear homogeneous equation are investigated. Using the Banach contraction mapping theorem, the existence and uniqueness of local and global solutions in specially constructed H¨older type spaces is proved. Abstract results are used for the study of an initial boundary value problem for a modified time-fractional order system of the phase field equations.