Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals

Ravi P. Agarwal; Vasile Lupulescu; Donal O'Regan; Ghaus ur Rahman

doi:10.1002/mana.201400010

Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals

Ravi P. Agarwal
, Vasile Lupulescu
, Donal O'Regan
, Ghaus ur Rahman

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

14 Citations (Scopus)

Abstract

The aim of this paper is to develop fractional calculus for vector-valued functions using the weak Riemann integral. Also, we establish the existence of weak solutions for a class of fractional differential equations with fractional weak derivatives.

Original language	English
Pages (from-to)	395-409
Number of pages	15
Journal	Mathematische Nachrichten
Volume	289
Issue number	4
DOIs	https://doi.org/10.1002/mana.201400010
Publication status	Published - 1 Mar 2016

Keywords

Caputo weak derivative
Fractional differential equation
Riemann-Pettis integral
Weak solution

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10.1002/mana.201400010

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title = "Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals",

abstract = "The aim of this paper is to develop fractional calculus for vector-valued functions using the weak Riemann integral. Also, we establish the existence of weak solutions for a class of fractional differential equations with fractional weak derivatives.",

keywords = "Caputo weak derivative, Fractional differential equation, Riemann-Pettis integral, Weak solution",

author = "Agarwal, \{Ravi P.\} and Vasile Lupulescu and Donal O'Regan and \{ur Rahman\}, Ghaus",

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T1 - Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals

AU - Agarwal, Ravi P.

AU - Lupulescu, Vasile

AU - O'Regan, Donal

AU - ur Rahman, Ghaus

PY - 2016/3/1

Y1 - 2016/3/1

N2 - The aim of this paper is to develop fractional calculus for vector-valued functions using the weak Riemann integral. Also, we establish the existence of weak solutions for a class of fractional differential equations with fractional weak derivatives.

AB - The aim of this paper is to develop fractional calculus for vector-valued functions using the weak Riemann integral. Also, we establish the existence of weak solutions for a class of fractional differential equations with fractional weak derivatives.

KW - Caputo weak derivative

KW - Fractional differential equation

KW - Riemann-Pettis integral

KW - Weak solution

UR - https://www.scopus.com/pages/publications/84961134280

U2 - 10.1002/mana.201400010

DO - 10.1002/mana.201400010

M3 - Article

SN - 0025-584X

VL - 289

SP - 395

EP - 409

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 4

ER -

Weak solutions for fractional differential equations in nonreflexive Banach spaces via Riemann-Pettis integrals

Abstract

Keywords

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