Complementary equations: a fractional differential equation and a Volterra integral equation
It is shown that a continuous, absolutely integrable function satisfies the initial value problem \[ D^{q}x(t) = f(t,x(t)), \qquad \lim_{t \to 0^+} t^{1-q}x(t) = x^{0} \qquad (0 < q < 1) \] on an interval $(0, T]$ if and only if it satisfies the Volterra integral equation \[ x(t) = x^...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3782 |