分数阶积分方程

The Franctional Order Integral Equations

对分数阶微分方程的初值问题所对应的分数阶积分方程ｚ（ｔ）＝∑ｌｋ＝０Ｃｋｋｌｔｋ＋（－λ）Γ（α）∫ｔ０（ｔ－ｓ）α－１ｚ（ｓ）ｄｓα≥１ｚ（ｔ）＝∑２ｌ－１ｋ＝０ＣｋГ（１＋ｋα２ｌ）ｔｋα／２ｌ＋（－λ）Г（α）∫ｔ０（ｔ－ｓ）α－１ｚ（ｓ）ｄｓｌ＝０，１，２，…

Using the Mellin transform and Fox functions,the solutions of fractional order integral equationsz(t)=∑lk=0C kk lt k+(-λ)Г(α)∫ t 0(t-s) α-1 z(s)ds α≥1and z(t)=∑2 l-1k=0C kГ(1+kα2 l)t kα/2 l +(-λ)Г(α)∫ t 0(t-s) α-1 z(s)ds l=0,1,2,… α≥0are foundz(t)=∑lk=0∑∞n=0C k(-λ) nГ(1+k+nα)t k+nα andz(t)=∑2 l-1k=0C k∑∞n=0(-λ) nГ(1+nα+kα2 l)t nα+kα2 l 