LYAPUNOV-TYPE INEQUALITIES FOR FRACTIONAL BOUNDARY VALUE PROBLEMS INVOLVING TWO GENERALIZED FRACTIONAL DERIVATIVES WITH RESPECT TO ANOTHER FUNCTION

This paper is devoted to the study of Dirichlet boundary value problems for fractional differential equations involving two types of fractional derivatives defined with respect to another function, introduced by Nieto et al. [22]. By constructing the corresponding generalized Green's functions and analyzing their structural properties, we derive necessary conditions for the existence of nontrivial solutions in the form of generalized Lyapunov-type inequalities. The results extend the classical Lyapunov inequality and contribute to the qualitative analysis of boundary value problems governed by generalized fractional derivatives.