Hyers-ulam stability in some differential equation models

This PhD thesis consists of nine chapters. In the first chapter of thesis, some basic information with regard to the subject of the thesis are given. In the second chapter, some scientific works that can be found in the literature, which are related to the thesis topic, are summarized briefly. In the third chapter of thesis, the materials and methods to be used in this thesis are introduced. In the fourth chapter of thesis, some basic definitions, theorems and lemmas with regard to the thesis topic are given. In the fifth chapter of the thesis, the stabilities of HU and HUR for a nonlinear Volterra integro-differential equation with multiple fixed lags are investigated by taking into account the Chebyshev norm definition and the results related to these are given. In the sixth chapter of the thesis, the results related to the stabilities of HU and GHUR for a nonlinear differential equation with multiple variable lags are obtained by taking into account the Chebyshev norm definition and the abstract Gronwall lemma. In the seventh chapter of the thesis, the results related to the stabilities of HU, HUR and -semi-HU for a Volterra integro-differential equation with order 1 iterated are obtained by taking into account the Bielecki metric definition. In the eighth chapter, the stability of HU of a fractional order equation with delay is investigated by taking into account the Bielecki metric definition. In the ninth chapter, the stability of HUR of a Volterra integro-differential equation with deviating argument is shown by taking into account the Bielecki norm definition and the Gronwall lemma. Finally, in the tenth chapter of thesis, discussion and conclusion with regard to content of this PhD thesis are given.