Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
2015 ◽
Vol 18
(1)
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Keyword(s):
AbstractIn We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given.
2020 ◽
Vol 21
(2)
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pp. 205-218
2019 ◽
Vol 2019
(1)
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2019 ◽
Vol 22
(4)
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pp. 1086-1112
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2009 ◽
Vol 2009
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pp. 1-11
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2014 ◽
Vol 51
(2)
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pp. 141-154
2019 ◽
Vol 9
(3)
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pp. 86-94