Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability

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• 作者：Ngo Van Hoa^a ; ^b ; ^{ngovanhoa@tdt.edu.vn} ; Vasile Lupulescu^c ; Donal O'Regan^d
• 关键词：Interval-valued functions ; Interval-valued Riemann&ndash ; Liouville fractional integral ; Interval-valued Caputo fractional derivative ; Interval-valued fractional differential equations ; Fractional Euler method ; Adams&ndash ; Bashforth&ndash ; Moulton method
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：1-34
• 全文大小：614 K
• 卷排序：309

文摘

In this paper interval-valued fractional differential equations (IFDEs) under Caputo generalized Hukuhara differentiability are introduced. We present existence and uniqueness results for IFDEs with a Krasnoselskii–Krein-type condition. The solution to interval-valued fractional initial value problems under Caputo-type interval-valued fractional derivatives by a modified fractional Euler method (MFEM) and a modified Adams–Bashforth–Moulton method (MABMM) is also presented.