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一類Riemann-Liouville分?jǐn)?shù)階時滯發(fā)展方程解的存在性

2023-07-28 03:27:16楊和白玉潔
關(guān)鍵詞:責(zé)任方程解白玉

楊和 白玉潔

摘要:利用上下解單調(diào)迭代方法討論了有序Banach空間中一類含Riemann-Liouville分?jǐn)?shù)階導(dǎo)數(shù)的時滯發(fā)展方程mild解的存在性,并通過一個具體的例子驗(yàn)證了抽象結(jié)論.

關(guān)鍵詞:Riemann-Liouville分?jǐn)?shù)階導(dǎo)數(shù);上下解;單調(diào)迭代技巧;時滯;加權(quán)函數(shù)

中圖分類號:O 175.15 文獻(xiàn)標(biāo)志碼:A 文章編號:1001-988Ⅹ(2023)04-0009-07

參考文獻(xiàn):

[1] GOU Hai-de,LI Yong-xiang,LI Qiang.Mixed monotone iterative technique for Hilfer fractional evolution equations with nonlocal conditions[J].J Appl Anal Comput,2020,10(5):1823.

[2] ZHANG Xu-ping,LI Yong-xiang.Monotone iterative technique for fractional partial differential equations with impulses[J].J Comput Anal Appl,2018,25(3):418.

[3] GOU Hai-de,LI Yong-xiang.The method of lower and upper solutions for impulsive fractional evolution equations in Banach spaces[J].J Korean Math Soc,2020,57(1):61.

[4] LI Qiang,WEI Mei.Monotone iterative technique for S-asymptotically periodic problem of fractional evolution equation with finite delay in ordered Banach space[J].J Math? Inequal,2021,15(2):521.

[5] GUO Yu-chen,SHU Xiao-bao,LI Yong-jin,et al.The existence and Hyers-Ulam stability of solution for an impulsive Riemann-Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1<β<2[J/OL].Bound Value Probl,2019,59,https://doi.org/10.1186/s13661-1172-6.

[6] ZHOU Yong,ZHANG Lu,SHEN Xiao-hui.Existence of mild solutions for fractional evolution equations[J].J Integral Equations Appl,2013,25(4):557.

[7] MOKKEDEM F Z.Approximate controllability for weighted semilinear Riemann Liouville fractional differential systems with infinite delay[J/OL].Differential Equations and Dynamical Systems,2020,[2020-02-20].https://doi.10.1007/s12591-020-00521-z.

[8] LIU Zhen-hai,LI Xiu-wen.Approximate controllability of fractional evolution systems with Riemann-Liouville fractional derivatives[J].SIAM J Control Optim,2015,53(4):1920.

[9] LI Qiang,WANG Guo-tao,WEI Mei.Monotone iterative technique for time-space fractional diffusion equations involving delay[J].Nonlinear Anal Model Control,2021,26(2):241.

[10] PAZY A.Semigroups of Linear Operators and Applications to Partial Differential Equations[M].New York:Springer-Verlag,1983.

[11] BANAS J,GOEBEL K.Measures of Noncompactness in Banach Spaces[J].New York:Marcel Dekker Inc,1980.

[12] HEINZ H P.On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions[J].Nonlinear Anal,1983,7(12):1351.

[13] ALQIFIARY Q H,JUNG S M.On the Hyers-Ulam stability of differential equations of second order[J].Abstr Appl Anal,2014,23:306.

[14] GOU Hai-de,LI Yong-xiang.Existence of mild solutions for impulsive fractional evolution equations with periodic boundary conditions[J].J Pseudo-Differ Oper Appl,2020,11(1):425.

(責(zé)任編輯 馬宇鴻)

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