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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.

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On the Fractional Pettis and Aumann-Pettis Integral for Multifunctions

100%

Ibrahim A.-G., Soliman A. M.

Commentationes Mathematicae

2006

tom 46

nr 2

Let \(\alpha\) be a positive real number. In the present paper we present the definition of the Aumann Pettis integral and the Pettis integral of order \(\alpha\) for multifunctions. The properties of these integrals and the relations between them are studied extensively. In particular, a Strassen type theorem in this case and continuation property are proved. Also, we give a version for Fatou's lemma and dominated convergence theorem for the Aumann-Pettis integral of order \(\alpha\) and for multifunctions.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Open Mathematics

1 Dong Q.

1 Fan Z.

1 Ibrahim A.-G.

1 Liu C.

1 Soliman A. M.

1 2016

1 2006

Wyniki wyszukiwania

Weighted fractional differential equations with infinite delay in Banach spaces

On the Fractional Pettis and Aumann-Pettis Integral for Multifunctions