The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus
2012 ◽
Vol 15
(2)
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Keyword(s):
The Mean
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AbstractWe generalize the classical mean value theorem of differential calculus by allowing the use of a Caputo-type fractional derivative instead of the commonly used first-order derivative. Similarly, we generalize the classical mean value theorem for integrals by allowing the corresponding fractional integral, viz. the Riemann-Liouville operator, instead of a classical (firstorder) integral. As an application of the former result we then prove a uniqueness theorem for initial value problems involving Caputo-type fractional differential operators. This theorem generalizes the classical Nagumo theorem for first-order differential equations.
2017 ◽
Vol 17
(4)
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pp. 661-678
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2002 ◽
Vol 32
(1)
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pp. 47-55
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Keyword(s):