Eur. Phys. J. Special Topics 226, 3501–3512 (2017)
https://doi.org/10.1140/epjst/e2018-00064-2

Regular Article

Variation of constant formula for the solution of interval differential equations of non-integer order

¹ Young Researchers and Elite Club, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Iran
² Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
³ Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey
⁴ Institute of Space Sciences, Magurele-Bucharest, Romania

^a e-mail: soheilsalahshour@yahoo.com

Received: 30 July 2017
Received in final form: 6 December 2017
Published online: 25 July 2018

Abstract

In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherits the classical properties from the first order derivative. Therefore, we propose in this research a new strategy to acquire interval solution of fractional interval differential equations (FIDEs) under interval fractional conformable derivative. This scheme is developed based on a variation of the constant formula to achieve the solution explicitly. The important characteristic of this technique is that it helps us to find a solution with decreasing length of its support which is critical for the solutions based on the interval or fuzzy notions. Two examples are experienced to illustrate our approach and validate it.