Fractional-order multivalued problems with non-separated integral-flux boundary conditions

In this paper, we study the existence of solutions for a new kind of boundary value problem of Caputo type fractional differential inclusions with non-separated local and nonlocal integral-flux boundary conditions. We apply appropriate fixed point theorems for multivalued maps to obtain the existence results for the given problems covering convex as well as non-convex cases for multivalued maps. We also include Riemann-Stieltjes integral conditions in our discussion. Some illustrative examples are also presented. The paper concludes with some interesting observations

Existence of multiple positive solutions of a nonlinear arbitrary order boundary value problem with advanced arguments

In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments \begin{equation*}\left\{\begin {array}{ll} D^\alpha_{0^+} u(t) +a(t)f(u(\theta(t)))=0,&0<t<1,~n-1<\alpha\le n,\\ u^{(i)}(0)=0,&i=0,1,2,\cdots,n-2,\\ ~[D^\beta_{0^+} u(t)]_{t=1}=0,&1\le \beta\le n-2, \end {array}\right.\end{equation*} where $n>3\,\, (n\in\mathbb{N}),~D^\alpha_{0^+}$ is the standard Riemann-Liouville fractional derivative of order $\alpha,$ $f: [0,\infty)\to [0,\infty),$ $a: [0,1]\to (0,\infty)$ and $\theta: (0,1)\to (0,1]$ are continuous functions. By applying fixed point index theory and Leggett-Williams fixed point theorem, sufficient conditions for the existence of multiple positive solutions to the above boundary value problem are established

A system of abstract measure delay differential equations

In this paper existence and uniqueness results for an abstract measure delay differential equation are proved, by using Leray-Schauder nonlinear alternative, under Carathéodory conditions

Monotone increasing multi-valued condensing random operators and random differential inclusions

In this paper, some random fixed point theorems for monotone increasing, condensing and closed multi-valued random operators are proved. They are then applied to first order ordinary nonconvex random differential inclusions for proving the existence of solutions as well as the existence of extremal solutions under certain monotonicity conditions

Qualitative aspects of Volterra integro-dynamic system on time scales

This paper deals with the resolvent, asymptotic stability and boundedness of the solution of time-varying Volterra integro-dynamic system on time scales in which the coefficient matrix is not necessarily stable. We generalize at time scale some known properties about asymptotic behavior and boundedness from the continuous case. Some new results for discrete case are obtained

Existence results for first order impulsive semilinear evolution inclusions

In this paper the concepts of lower mild and upper mild solutions combined with a fixed point theorem for condensing maps and the semigroup theory are used to investigate the existence of mild solutions for first order impulsive semilinear evolution inclusions

Existence of solutions of boundary value problems for functional differential equations

In this paper, using a simple and classical application of the Leray-Schauder degree theory, we study the existence of solutions of the following boundary value problem for functional differential equations x″(t)+f(t,xt,x′(t))=0,   t∈[0,T]x0+αx′(0)=hx(T)+βx′(T)=η where f∈C([0,T]×Cr×ℝn,ℝn), h∈Cr, η∈ℝn and α, β, are real constants

Some results on boundary value problems for functional differential equations

Existence results for a second order boundary value problem for functional differential equation, are givn. The results are based on the nonlinear Alternative, of Leray-Schauder and rely on a priori bounds on solutions. These results are generalizations of recent results from ordinary differential equations and complete our earlier results on the same problem

On nonresonance impulsive functional nonconvex valued differential inclusions

summary:In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces