数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 661-672.doi: 10.1016/S0252-9602(11)60266-X

• 论文 • 上一篇    下一篇

FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

Hussein A.H.Salem   

  1. Department of Mathematics, Faculty of Sciences, Alexandria University, Egypt;Department of Mathematics, Faculty of Sciences and Arts, Taibah University, Saudia Arabia
  • 收稿日期:2008-08-19 修回日期:2010-04-09 出版日期:2011-03-20 发布日期:2011-03-20

FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

Hussein A.H.Salem   

  1. Department of Mathematics, Faculty of Sciences, Alexandria University, Egypt;Department of Mathematics, Faculty of Sciences and Arts, Taibah University, Saudia Arabia
  • Received:2008-08-19 Revised:2010-04-09 Online:2011-03-20 Published:2011-03-20

摘要:

In this article, we  investigate the existence of Pseudo solutions for some  fractional order  boundary value problem  with integral
boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems
constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value
problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function.  To  encompass the full scope of this article, we give an example illustrating the main result.

关键词: Fractional calculus, Pseudo solution, boundary value problem, Pettis integrals

Abstract:

In this article, we  investigate the existence of Pseudo solutions for some  fractional order  boundary value problem  with integral
boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems
constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value
problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function.  To  encompass the full scope of this article, we give an example illustrating the main result.

Key words: Fractional calculus, Pseudo solution, boundary value problem, Pettis integrals

中图分类号: 

  • 26A33