Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces

Abstract

Abstract. The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

Nonlinear multi-order fractional differential equations with periodic/anti-periodic boundary conditions

“…In view of Remark 3.1, we can also prove the following existence and uniqueness theorems for the boundary value problems (3.1)-(3.2) and (3.1)-(3.3), in the same lines as given in Ref. [5]. …”

“…al [4] have introduced and studied a new concept of periodic boundary conditions in the context of Riemann-Liouville derivatives. Existence results for non-linear fractional differential equations with integral boundary conditions [5] and anti-periodic fractional boundary conditions [1], [15] have been investigated. For partially ordered metric spaces, Baleanu et.…”

Weak solutions for some nonlinear fractional differential equations with fractional integral boundary conditions in Banach spaces

“…The strong measure of noncompactness was considered first by Banas and Goebel [29] and subsequently developed and used in many papers; see, for example, Akhmerov et al [30], Alvàrez [31], Belmekki and Mekhalfi [32], Benchohra, Henderson and Seba [33], Guo, Lakshmikantham and Liu [34], and the references therein. Recently, there are also many results on weak solutions of nonlinear fractional differential equations; see [33,35,36,37,38,39] and the references therein.…”

Weak Solutions of Fractional Order Differential Equations via Volterra-Stieltjes Integral Operator

“…Fractional order derivatives have the memory property and can describe many phenomena that integer order derivatives cant characterize. Only a few papers consider fractional differential equations in reflexive Banach spaces with the weak topology [6,7,14,22,23]. Here we study the existence of weak solutions of the Volterra-Stieltjes integral equation with the initial data…”