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In this paper we provide sufficient conditions for the existence of solutions of initial value problem for perturbed hyperbolic differential inclusions of fractional order involving Caputo fractional derivative by using the mixed generalized Lipschitz and Carathéodory's conditions. [ABSTRACT FROM AUTHOR]

In the paper, we prove the existence of solutions and Carathéodory's type solutions of the dynamic Cauchy problem xΔ(t) = f(t; x(t)); t ϵ T; x(0) = x0; where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xn) in T and xn → ∞) and f is continuous or satisfies Carathéodory's conditions and some conditions expressed in terms of measures of noncompactness. The Sadovskii fixed point theorem and Ambrosetti's lemma are used to prove the main result. The results presented in the paper are new not only for Banach valued functions, but also for real-valued functions. [ABSTRACT FROM AUTHOR]

In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carathéodory and certain monotonicity conditions. [ABSTRACT FROM AUTHOR]

In this paper we use the upper and lower solutions method combined with Schauder's Fxed point theorem and a Fxed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions. [ABSTRACT FROM AUTHOR]

This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type. [ABSTRACT FROM AUTHOR]

In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Riemann-Liouville fractional order, by using an extension of the Burton-Kirk fixed point theorem in the case of a Fréchet space. [ABSTRACT FROM AUTHOR]

In this paper we prove existence theorems for integro - differential equations xΔ(t) = f(t, x(t), ∫ 0 t k(t, s, x(s))Δs), x(0) = x0 t ∊ Ia = [0, a] ∩ T, a ∊ R+, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. Functions f, k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral. Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale. [ABSTRACT FROM AUTHOR]

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type. [ABSTRACT FROM AUTHOR]

In this paper, we study Φ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multivalued right-hand side. The nonlinearity satisfies either a Nagumotype growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan- Colombo selection theorem respectively. Two applications to a problem from control theory are provided. [ABSTRACT FROM AUTHOR]

In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems. [ABSTRACT FROM AUTHOR]

In this paper we consider the first order difference equation in a Banach space (Multiple line equation(s) cannot be represented in ASCII text). We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation (Multiple line equation(s) cannot be represented in ASCII text) and give conditions when this equation has solutions. In this note we extend the results from [8, 9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered. [ABSTRACT FROM AUTHOR]

In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established. [ABSTRACT FROM AUTHOR]

In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for single valued mappings satisfying an implicit relation on space with two metrics. In addition we give a homotopy result using our theorems. [ABSTRACT FROM AUTHOR]

In this paper, we prove existence and controllability results for first and second order semilinear neutral functional differential inclusions with finite or in finite delay in Banach spaces, with nonlocal conditions. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families. [ABSTRACT FROM AUTHOR]

In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space. [ABSTRACT FROM AUTHOR]