Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

Abstract

In this paper, we study the existence of mild solutions for a class of semilinear fractional differential equations with nonlocal conditions in Banach spaces. The results are obtained by using convex-power condensing operator and fixed point theory. An example is presented to illustrate the main result.MSC 2010 : Primary 26A33: Secondary 33E12

L P -solutions for fractional integral equations

“…259-276 , DOI: 10.2478/s13540-014-0166-4 of L p -solutions of Volterra-Urysohn functional equations of fractional type were given in [16]. Existence results for fractional differential equations under compactness type condition were discussed in [1], [2] and [7]. In this article we study L p -solutions of fractional integral equations in Banach spaces using a compactness type condition.…”

Fractional neutral stochastic differential equations driven by α-stable process

“…see, for example, [14,28]. Motivated by this result and noting Definitions 2.4 and 2.5, we present the following definition of mild solutions to (1.1).…”

Stochastic delay fractional evolution equations driven by fractional Brownian motion

“…We refer to [6] about the definition of mild solutions to (3.1), for convenience, the details is presented in the following. Since the coefficient operator A is the infinitesimal generator of a C 0 -semigroup T (t), there exists constants N ≥ 1, ω ≥ 0, such that T (t) ≤ Ne ωt , t ≥ 0.…”

“…The Laplace transform of the Caputo fractional derivative is given by 6) whereû(λ) is the Laplace transform of u defined bŷ…”