数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 758-772.doi: 10.1016/S0252-9602(13)60036-3

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EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL´S INEQUALITY IN BANACH SPACES

Dimplekumar N. CHALISHAJAR|K. KARTHIKEYAN   

  1. Department of Mathematics and Computer Science, Virginia Military Institute (VMI) 417 Mallory Hall, Lexington, VA 24450, USA; Department of Mathematics, KSR College of Technology, Tiruchengode-637 215, Tamilnadu, India
  • 收稿日期:2012-03-05 出版日期:2013-05-20 发布日期:2013-05-20
  • 基金资助:

    This work is supported by Grant In Aid research fund of Virginia Military Instittue, USA.

EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL´S INEQUALITY IN BANACH SPACES

Dimplekumar N. CHALISHAJAR|K. KARTHIKEYAN   

  1. Department of Mathematics and Computer Science, Virginia Military Institute (VMI) 417 Mallory Hall, Lexington, VA 24450, USA; Department of Mathematics, KSR College of Technology, Tiruchengode-637 215, Tamilnadu, India
  • Received:2012-03-05 Online:2013-05-20 Published:2013-05-20
  • Supported by:

    This work is supported by Grant In Aid research fund of Virginia Military Instittue, USA.

摘要:

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ (n−1, n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder´s inequality, a suitable singular Gronwall´s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

关键词: Boundary value problems, fractional order integro-differential equations, bound-ary value problems, existence and uniqueness, singular gronwall inequality, fixed point theorem

Abstract:

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ (n−1, n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder´s inequality, a suitable singular Gronwall´s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

Key words: Boundary value problems, fractional order integro-differential equations, bound-ary value problems, existence and uniqueness, singular gronwall inequality, fixed point theorem

中图分类号: 

  • 26A33