Opuscula Math. 36, no. 4 (2016), 541-556

Opuscula Mathematica

On fractional random differential equations with delay

Ho Vu
Nguyen Ngoc Phung
Nguyen Phuong

Abstract. In this paper, we consider the existence and uniqueness of solutions of the fractional random differential equations with delay. Moreover, some kind of boundedness of the solution is proven. Finally, the applicability of the theoretical results is illustrated with some real world examples.

Keywords: sample path fractional integral, sample path fractional derivative, fractional differential equations, sample fractional random differential equations, Caputo fractional derivative, delay.

Mathematics Subject Classification: 26A33, 47H40, 60H25.

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  • Ho Vu
  • Banking University, Faculty of Economic Mathematics, Ho Chi Minh City, Vietnam
  • Nguyen Ngoc Phung
  • Nguyen Phuong
  • Communicated by Palle E.T. Jorgensen.
  • Received: 2014-11-15.
  • Revised: 2015-12-24.
  • Accepted: 2015-12-24.
  • Published online: 2016-04-01.
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Cite this article as:
Ho Vu, Nguyen Ngoc Phung, Nguyen Phuong, On fractional random differential equations with delay, Opuscula Math. 36, no. 4 (2016), 541-556, http://dx.doi.org/10.7494/OpMath.2016.36.4.541

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