Fractional calculus and fractional differential equations in nonreflexive Banach spaces

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

doi:10.1016/j.cnsns.2013.10.010

Fractional calculus and fractional differential equations in nonreflexive Banach spaces

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

Mathematics

Texas A&M University
Constantin Brancusi University
Government College University Lahore

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

42 Citations (Scopus)

Abstract

In this paper we establish an existence result for the fractional differential equation. Dpαy(t)=f(t,y(t)),y(0)=y0,where Dpαy(·) is a fractional pseudo-derivative of a weakly absolutely continuous and pseudo-differentiable function y(·) :. T→ E, the function f(t,. ·). :T×. E→ E is weakly-weakly sequentially continuous for every t∈. T and f(· y(·)) is Pettis integrable for every weakly absolutely continuous function y(·) : T→ E, T is a bounded interval of real numbers and E is a nonreflexive Banach space.

Original language	English
Pages (from-to)	59-73
Number of pages	15
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	20
Issue number	1
DOIs	https://doi.org/10.1016/j.cnsns.2013.10.010
Publication status	Published - 1 Jan 2015

Keywords

Existence
Fractional differential equation
Pettis integral
Pseudo-derivative

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Agarwal, RP,Lupulescu, V,O'Regan, D,Rahman, GU

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10.1016/j.cnsns.2013.10.010

Cite this

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abstract = "In this paper we establish an existence result for the fractional differential equation. Dpαy(t)=f(t,y(t)),y(0)=y0,where Dpαy(·) is a fractional pseudo-derivative of a weakly absolutely continuous and pseudo-differentiable function y(·) :. T→ E, the function f(t,. ·). :T×. E→ E is weakly-weakly sequentially continuous for every t∈. T and f(· y(·)) is Pettis integrable for every weakly absolutely continuous function y(·) : T→ E, T is a bounded interval of real numbers and E is a nonreflexive Banach space.",

keywords = "Existence, Fractional differential equation, Pettis integral, Pseudo-derivative",

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T1 - Fractional calculus and fractional differential equations in nonreflexive Banach spaces

AU - Agarwal, Ravi P.

AU - Lupulescu, Vasile

AU - O'Regan, Donal

AU - ur Rahman, Ghaus

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this paper we establish an existence result for the fractional differential equation. Dpαy(t)=f(t,y(t)),y(0)=y0,where Dpαy(·) is a fractional pseudo-derivative of a weakly absolutely continuous and pseudo-differentiable function y(·) :. T→ E, the function f(t,. ·). :T×. E→ E is weakly-weakly sequentially continuous for every t∈. T and f(· y(·)) is Pettis integrable for every weakly absolutely continuous function y(·) : T→ E, T is a bounded interval of real numbers and E is a nonreflexive Banach space.

AB - In this paper we establish an existence result for the fractional differential equation. Dpαy(t)=f(t,y(t)),y(0)=y0,where Dpαy(·) is a fractional pseudo-derivative of a weakly absolutely continuous and pseudo-differentiable function y(·) :. T→ E, the function f(t,. ·). :T×. E→ E is weakly-weakly sequentially continuous for every t∈. T and f(· y(·)) is Pettis integrable for every weakly absolutely continuous function y(·) : T→ E, T is a bounded interval of real numbers and E is a nonreflexive Banach space.

KW - Existence

KW - Fractional differential equation

KW - Pettis integral

KW - Pseudo-derivative

UR - https://www.scopus.com/pages/publications/84905378740

U2 - 10.1016/j.cnsns.2013.10.010

DO - 10.1016/j.cnsns.2013.10.010

M3 - Article

SN - 1007-5704

VL - 20

SP - 59

EP - 73

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 1

ER -

Fractional calculus and fractional differential equations in nonreflexive Banach spaces

Abstract

Keywords

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