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Weighted fractional differential equations with infinite delay in Banach spaces

100%

Dong Q., Liu C., Fan Z.

Open Mathematics

2016

tom 14

nr 1

370-383

This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed.

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

75%

Raffoul Y., Rai H.

Nonautonomous Dynamical Systems

2016

tom 3

nr 1

14-23

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]

Ograniczanie wyników

1 Nonautonomous Dynamical Systems

1 Open Mathematics

1 Dong Q.

1 Fan Z.

1 Liu C.

1 Raffoul Y.

1 Rai H.

2 2016

Wyniki wyszukiwania

Weighted fractional differential equations with infinite delay in Banach spaces

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals