Generalized phi-dichotomous linear part for a class of generalized differential equations

Abstract

A dichotomy: ordinary or exponential, is a category of conditional stability. In this disquisition, we deal with nonlinear fractional differential equations (NFDE) involving generalized $\Phi$-exponential and $\Phi$-ordinary dichotomous (in
the sense of fractional calculus) linear part in a Banach space. By employing of the Banach fixed point principle, the satisfactory conditions are located for the existence of $\Phi$-bounded outcomes of these equations in the real case.