MSC: 34A37 34A60 34G25 34K30 34K35 34K45 93B05 Keywords: Nondensely defined operator Impulsive semilinear differential inclusion Fixed point Integral solutions Extremal solution ControllabilityIn this paper, we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators. The question of controllability of these equations and the topological structure of the solutions set are considered too.

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In this paper, we study the existence of solutions for hybrid fractional differential equations involving fractional Caputo derivative of order 1 < α ≤ 2. Our results rely on a hybrid fixed point theorem for a sum of three operators due to Dhage. An example is provided to illustrate the theory.

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined impulsive semilinear functional differential equations with state-dependent delay in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators.