Résumé:
Themaingoalofthisthesisistopresentasetresultsontheexistence,uniquenessandsta-
bilityofcertainclassesoftheinitialvalueproblemsandboundaryvalueproblemsforfrac-
tional q-differenceequationsandimpulsivefractional q-differenceequationsinvolving
Caputo’sfractional q-derivative.Theresultshavebeenprovenanalytically,wheretheex-
istenceresultsarebasedonsomeclassicalfixedpointtheorems(Banach,Schaefer,Kras-
noselskii, Non-linearalternativeofLeray-Schauder)aswellasMönch’sfixedpointthe-
oremcombinedwiththetechniqueofKuratowski’smeasureofnoncompactness,while
thestabilityresultsdependonthetechniquesofUlam-HyersstabilityandUlam-Hyers-
Rassiasstability.Tosupportourresults,weprovidedifferentillustrativeexamplesineach
chapter.
