In this paper we prove existence and uniqueness results to three point boundary value problems associated with singular system of first order differential equations by the use of generalized inverses of matrices.

In this article, we focus our study on a nondifferentiable minimax fractional programming problem and establish weak, strong and strict converse duality theorems under generalized higher order (F , α, ρ, d)-Type I assumptions. Our results extend and unify some of the known results in the literature.

In this paper, we study the existence criteria for Ψ-bounded solutions of Sylvester matrix dynamical systems on time scales. The advantage of studying this system is it unifies continuous and discrete systems. First, we prove a necessary and sufficient condition for the existence of atleast one Ψ-bounded solution for Sylvester matrix dynamical systems on time scales, for every Lebesgue Ψdeltaintegrable function F, on time scale T +. Further, we obtain a result relating to asymptotic behavior of Ψ-bounded solutions of this equation. The results are illustrated with suitable examples.

In this paper, we provide a way to combine matrix Lyapunov systems with fuzzy sets to form a new system called fuzzy dynamical matrix Lyapunov system and obtain a sufficient condition for the controllability of this system.

In this work, we develop the criteria for existence of Ψ- bounded solutions of system of linear dynamic equations on time scales. The advantage of results in this dynamical system is it unifies discrete as well as continuous systems. Initially, we develop if and only if conditions for the existence of at least one Ψ-bounded solution for linear dynamic equation y∆(τ ) = P (τ )y +g(τ ), for each Ψ- delta integrable  Lebesgue function g, on time scale T +. Later, we obtain asymptotic nature of Ψ-bounded solutions of dynamical system. Also we provided the examples for supporting the results.AMS Subject Classification: 74H20, 34N05, 34C11