In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is $L^{1}_{\alpha }$-carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.

In this article, we study the existence of solutions to systems of first-order $\nabla$-dynamic equations on time scales with periodic boundary or terminal value conditions. where the right member of the system is $\nabla$-Carathéodory. We employ the method of solution-tube and Schauder's fixed-point theorem.

We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an initial value problem characterized by structural Nabla derivatives on timescales. Furthermore, some features of the new operator are proven and illustrated by using concrete examples.

In this article, we define and study the nabla conformable fractional derivative and nabla conformable fractional integral on time scales. Many basic properties of the theory are proved.

In this article, we study the existence of solutions to systems of first-order $\nabla$-dynamic inclusions on time scales with terminal or periodic boundary conditions. We employ the method of solution-tube and Kakutani fixed point Theorem.