Comparison principles for a class of general integro-differential inequalities with applications

Mohammed Al-Refai1, Arran Fernandez2
1Department of Mathematics, Yarmouk University, Irbid, 21163, Jordan
2Department of Mathematics, Eastern Mediterranean University, 99628, Famagusta, Northern Cyprus, via Mersin 10, Turkey

Tóm tắt

AbstractComparison principles for fractional differential equations have been investigated in many papers using different types of fractional integral and derivative operators. We here prove the strongest such results so far, for a very broad class of operators that is even more general than those with Sonine kernels. Starting from inequalities valid at global extrema, we obtain comparison principles for these general operators, which are applied to prove bounds on solutions to related integro-differential equations. Many results in the literature will be considered as particular cases of the current study.

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