Existence Of Solutions To Boundary Value Problems For Fractional Differential Equations At Resonance

For the past few years, the fractional differential equations has made importantapplication and development in the area of Control,engineering,physics,mechanics,chemistry and other fields.Meanwhile,a number of achievements have emerged about thetheoretical research of the boundary value problems of fractional differential equations. Inaddition,Experts and scholars at home and abroad had extensive attention in The fractionaldifferential equations with p-Laplacian operator, The research in this aspect also hadachieved fruitful results.On the base of existing literature and previous research, this dissertation,using theMawhin theorem and popularize(Weigao,Ge,etc),discusses the existence of solutions forconcrete fractional differential equation boundary value problems with resonance fromvarious angles and the solvability for fractional differential equations possessingp-Laplacian operator with resonance.First of all,the introduction part introduces the research background, researchsignificance and the current research status of the overseas and domestic about thefractional differential equation boundary value problems.Secondly, under the Riemann-Stieltjesthis integral boundary condition, thisdissertation,by using Mawhin overlap theory,discusses the existence of solutions for(n1,1)conjugate boundary value problems with resonance,where the non-linear itemmaybe is not consecutive.In the end,by using the overlap theory and the projection operator establishedappropriately. the writer makes an effort to discuss the solvability for fractional differentialequations possessing p-Laplacian operator with resonance.