数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1568-1578.doi: 10.1007/s10473-019-0608-5

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ON THE EXISTENCE AND STABILITY OF BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATION WITH HILFER-KATUGAMPOLA FRACTIONAL DERIVATIVE

E. M. ELSAYED1,2, S. HARIKRISHNAN3, K. KANAGARAJAN3   

  1. 1. Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;
    2. Department of Mathematics, Faculty of Science Mansoura University, Mansoura 35516, Egypt;
    3. Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, Tamilnadu, India
  • 收稿日期:2018-07-17 修回日期:2019-02-11 出版日期:2019-12-25 发布日期:2019-12-30
  • 通讯作者: E. M. ELSAYED,E-mail:emmelsayed@yahoo.com E-mail:emmelsayed@yahoo.com
  • 作者简介:S. HARIKRISHNAN,E-mail:hkkhari1@gmail.com;K. KANAGARAJAN,E-mail:kanagarajank@gmail.com
  • 基金资助:
    This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. KEP-Msc-9-130-39.

ON THE EXISTENCE AND STABILITY OF BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATION WITH HILFER-KATUGAMPOLA FRACTIONAL DERIVATIVE

E. M. ELSAYED1,2, S. HARIKRISHNAN3, K. KANAGARAJAN3   

  1. 1. Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;
    2. Department of Mathematics, Faculty of Science Mansoura University, Mansoura 35516, Egypt;
    3. Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, Tamilnadu, India
  • Received:2018-07-17 Revised:2019-02-11 Online:2019-12-25 Published:2019-12-30
  • Contact: E. M. ELSAYED,E-mail:emmelsayed@yahoo.com E-mail:emmelsayed@yahoo.com
  • Supported by:
    This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. KEP-Msc-9-130-39.

摘要: In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.

关键词: Hilfer-Katugampola fractional derivative, boundary condition, existence, Ulam stability

Abstract: In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.

Key words: Hilfer-Katugampola fractional derivative, boundary condition, existence, Ulam stability

中图分类号: 

  • 26A33