Existence and attractivity theorems for nonlinear hybrid fractional differential equations with anticipation and retardation

被引：0

作者：

Dhage B.C. ^{[1
]}

机构：

[1] Kasubai, Gurukul Colony, Thodga Road, Ahmedpur, Latur, Maharashtra

来源：

Journal of Nonlinear Functional Analysis | 2020年 / 2020卷 / 01期

关键词：

Attractivity of solutions; Dhage fixed point theorem; Existence theorem; Hybrid differential equation;

D O I：

10.23952/JNFA.2020.47

中图分类号：

学科分类号：

摘要：

In this paper, we establish an existence result and a global attractivity result for the mild solutions of a nonlinear quadratic hybrid fractional differential equation with the Caputo derivative on the unbounded intervals of the real line with the mixed arguments of anticipation and retardation. The hybrid fixed point theorem of Dhage is used in the analysis of our nonlinear differential problem. A positivity result is also obtained under some usual conditions. © 2020 Journal of Nonlinear Functional Analysis.

引用

共 22 条

[1]

Dhage B.C., Some characterizations of nonlinear first order differential equations on unbounded intervals, Differ. Equ. Appl, 2, pp. 151-162, (2010)

[2]

Dhage B.C., Global asymptotic attractivity and stability theorems for nonlinear Caputo fractional differential equations, J. Frac. Cal. Appl, 12, pp. 223-237, (2021)

[3]

Dhage B.C., Dhage S.B., Sarkate S.D., Attractivity and existence results for hybrid differential equations with anticipation and retardation, J. Math. Comput. Sci, 4, 2, pp. 206-225, (2014)

[4]

Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, (2006)

[5]

Podlubny I., Fractional Differential Equations, (1999)

[6]

Hilfer R., Applications of Fractional Calculus in Physics, (2000)

[7]

Dhage B.C., Remarks on two fixed point theorems involving the sum and product of two operators, Comptut. Math. Appl, 46, pp. 1779-1785, (2003)

[8]

Dhage B.C., Asymptotic stability of nonlinear functional integral equations via measures of noncompactness, Commun. Appl. Nonlinear Anal, 15, pp. 89-101, (2008)

[9]

Cichon M., Salem H.A.H., On the solutions of Caputo-Hadamard Pettis-type fractional differential equations, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM, 113, pp. 3031-3053, (2019)

[10]

Cichon M., Salem H.A.H., On the lack of equivalence between differential and integral forms of the Caputo-type fractional problems, J. Pseudo-Differ. Oper. Appl, 11, pp. 1869-1895, (2020)

← 1 2 3 →