Existence theory for ( k , ψ)-Caputo fractional differential inclusions with multi-point closed fractional boundary conditions

This paper examines a class of (k, ψ)-Caputo type fractional differential inclusions complemented with nonlocal multi-point closed fractional boundary conditions. Both convex and non-convex cases of multivalued maps are addressed in this study. For upper semicontinuous, convex-valued maps satisfying the L 1 -Carathéodory condition, we establish an existence theorem by means of the Leray–Schauder nonlinear alternative for multivalued operators. In the non-convex setting—specifically when the multivalued map is Lipschitz continuous and contractive—existence results are obtained via the Covitz–Nadler fixedpoint principle. To illustrate the effectiveness of the obtained theoretical work, examples are presented for highlighting both analytical and practical relevance of the fractional boundary value problem under consideration.