# Existence results for fractional-order differential equations with nonlocal multi-point-strip conditions involving Caputo derivative

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, 2015:348

First Online: 11 November 2015Received: 10 October 2015Accepted: 02 November 2015

Abstract

In this paper, we investigate the existence and uniqueness of solutions for a differential equation of fractional-order \q \in1, 2\ subject to nonlocal boundary conditions involving Caputo derivative of the form $$x0=\delta x\sigma,\qquad a {}^{c}D^{\mu} x \varrho {1}+b {}^{c}D^{\mu} x\varrho {2}=c \int {\beta {1}}^{\beta {2}} {}^{c}D^{\mu} xs \,ds,$$\0 < \varrho {1} < \sigma< \beta {1} < \beta {2} < \varrho {2} <1\, \0<\mu<1\, and δ, a, b, c are real constants. We make use of some standard tools of fixed point theory to obtain the desired results which are well illustrated with the aid of examples.Keywordsfractional order derivative nonlocal conditions strip existence fixed point MSC34A08 34B15  Download fulltext PDF

Autor: Bashir Ahmad - Ahmed Alsaedi - Alaa Alsharif