【摘要】：近年來,分?jǐn)?shù)階微分方程在許多學(xué)科領(lǐng)域都起到了至關(guān)重要的作用,如生物學(xué)、化學(xué)、工程學(xué)、物理學(xué)等等,從而吸引了越來越多的學(xué)者參與到該問題的研究中來,并取得了許多成果.本文主要研究了一類分?jǐn)?shù)階微分方程的邊值問題和一類分?jǐn)?shù)階脈沖微分方程的初值問題以及一類分?jǐn)?shù)階微分方程偽漸近周期解的存在性.首先,我們考慮以下非線性多基點(diǎn)分?jǐn)?shù)階脈沖微分方程的三點(diǎn)邊值問題,其中 α ∈(1,2),β,γ2 ∈(0,1),α-∈(1,2).cD 表示基點(diǎn)為 t = tk(k = 1,2,….,m)的Caputo分?jǐn)?shù)階導(dǎo)數(shù).Ik,Ik ∈ C(R,R),R表示實(shí)數(shù)空間.{tk}滿足0 = t0t1…tmtm+1 = T,△x(tk)表示函數(shù)x在tk處的跳躍,△x(tk)=x(tk+)-(tk-),其中x(tk+),x(tk-)分別表示x(t)在t=tk處的右極限和左極限.△x'(tk)的意義與Ax(t)類似.我們利用Schauder不動(dòng)點(diǎn)定理研究了該問題解的存在性.其次,我們考慮以下帶非局部延遲的分?jǐn)?shù)階脈沖微分方程,其中δ,T0,cD*α表示基點(diǎn)為t=tk(k = 1,2,….,m)的Caputo分?jǐn)?shù)階導(dǎo)數(shù);即對(duì)所有的t ∈(tk,tk+1],cD*α|(tk,tk+1]u(t)=c Dlkαku(t).A:D(A)(?)X → X 是復(fù) Banach空間X中的解析預(yù)解族{Sα(t)}t≥0的生成元.后面我們將給出f:J×D×X→X的具體假設(shè).此處D={ψ:[-0]→ X,ψ(s)除有限個(gè)點(diǎn)外處處連續(xù),ψ(s+)存在且ψ(s-)= ψ(s)}.g:→ ∈ D.{tk} 滿足 0 = t0t1…tptp+1 =T,Ik:X → X(k = 1,2,…,p)是脈沖函數(shù),△x(tk)表示函數(shù)x在tk處的跳躍,△x(tk)= x(tk+)-x(tk-),其中x(tk+),x(tk-)分別表示x在tk處的右極限和左極限.對(duì)任意定義在區(qū)間[-δ,T]\{t1,t2 …,tp}上的連續(xù)函數(shù)x和任意t ∈[0,T],我們用xt表示D中的元素,且定義如下:對(duì)(?)∈[-δ,0,,x(((?))=x(t+(?).最后,我們考慮以下Banach空間X上的分?jǐn)?shù)階微分方程初值問題,其中q ∈(0,1),cD0q+表示Caputo分?jǐn)?shù)階導(dǎo)數(shù),A是Banach空間X中的閉線性算子.我們利用算子半群理論和壓縮映射原理討論了該問題的偽漸近周期性解.
[Abstract]:In recent years, fractional differential equations have played an important role in many disciplines, such as biology, chemistry, engineering, physics and so on, thus attracting more and more scholars to participate in the study of this problem. Many achievements have been made. In this paper, the existence of pseudo-asymptotic periodic solutions for a class of fractional differential equations and a class of fractional impulsive differential equations are studied. First of all, we consider the following three point boundary value problems for nonlinear fractional impulsive differential equations of multiple basis points, where 偽 鈭，

本文編號(hào)：2260204