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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.

Existence results for fractional integro-differential inclusions with state-dependent delay

64%

Siracusa G., Henríquez H. R., Cuevas C.

Nonautonomous Dynamical Systems

2017

tom 4

nr 1

62-77

In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

Ograniczanie wyników

1 Nonautonomous Dynamical Systems

1 Open Mathematics

1 Cuevas C.

1 Dong Q.

1 Fan Z.

1 Henríquez H. R.

1 Liu C.

1 Siracusa G.

1 2017

1 2016

Wyniki wyszukiwania

Weighted fractional differential equations with infinite delay in Banach spaces

Existence results for fractional integro-differential inclusions with state-dependent delay