A New Kind of Nonlocal-integral Fractional Boundary Value Problems

详细信息    查看全文

• 作者：Bashir Ahmad ; Sotiris K. Ntouyas
• 关键词：Fractional differential equations ; Nonlocal ; Integral ; Boundary conditions ; Fixed point
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：39
• 期：4
• 页码：1343-1361
• 全文大小：516 KB
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：39

文摘

In this paper, we discuss a new class of nonlocal boundary value problems of fractional differential equations and inclusions with a new integral boundary condition. This new boundary condition states that the value of the unknown function at an arbitrary (local) point \(\xi \) is proportional to the contribution due to a sub-strip of arbitrary length \((1-\eta ),\) that is, \(x(\xi )=a \int _{\eta }^{1}x(s)\mathrm{d}s,\) where \(0< \xi < \eta <1\) and a is constant of proportionality. The existence of solutions for the given problems is shown by means of contraction mapping principle, a fixed point theorem due to O’Regan and nonlinear alternative for multivalued maps. The results are well illustrated with the aid of examples.