On some fractional differential problems of variable order

Abstract

Themainobjectiveofthisworksconcernssomeresultsofexistenceandstabilityofsolutionsofboundrayvalueproblemsofvariable-orderCaputotypefractionaldifferntialequation.Allresultsinthisstudyareestablishedwiththehelpofthegeneralizedintervalsandpiecewiseconstantfunction,weconverttheCaputofractionalvariableordertoanequivalentstandardCaputo of the fractional constant order.We illustrate our main results by adifferentexamplestovalidateourstudy.

L’objectifprincipaldecetravailconcernequelquesr´esultatsd’existenceetde stabilit´edesolutionsd’´equationdiff´erentiellefractionnairedetypeCaputod’ordre variable.Touslesr´esultatsdecette´étudesont´établis`al’aidedes intervallesg´en´eralis´esetdelafonctionconstanteparmorceaux,nouscon- vertissonsl’ordrevariablefractionnairedeCaputoenunCaputostandard ´equivalentdel’ordreconstantfractionnaire.Nousillustronsnosprincipaux r´esultatspardiff´erentsexemplespourvalidernotre´etude.