A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

2007
*
Journal of Applied Mathematics
*

We prove

doi:10.1155/2007/31572
fatcat:7ysbc6q7ufezzi3vhgxhtruszi
*existence*theorems*for*the*integrodifferential*equationx'(t)=f(t,x(t),∫0tk(t,s,x(s))ds),x(0)=x0,t∈Ia=[0,a],a>0, wheref,k,xare functions with values*in*a*Banach*spaceEand the*integral*is taken ...*in*the sense of HL. ... This means that there*exists*a solution of the problem (1.1). Aneta Sikorska-Nowak 11 ...##
###
Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions

2018
*
International Journal of Differential Equations
*

*integrodifferential*

*equations*. ... By combining the techniques of fractional calculus with measure of weak noncompactness

*and*fixed point theorem, we establish the

*existence*of weak solutions of multipoint boundary value problem

*for*fractional ... Introduction

*In*recent years, fractional differential

*equations*

*in*

*Banach*

*spaces*have been studied

*and*a few papers consider fractional differential

*equations*

*in*reflexive

*Banach*

*spaces*equipped with the ...

##
###
Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals

2010
*
Abstract and Applied Analysis
*

The functions are weakly-weakly sequentially continuous with values

doi:10.1155/2010/836347
fatcat:votmfjwhgzayhg2hgfd3rx4mnu
*in*a*Banach**space*,*and*the*integral*is taken*in*the sense of*Henstock*-*Kurzweil*-Pettis delta*integral*. ... This*integral*generalizes the*Henstock*-*Kurzweil*delta*integral**and*the Pettis*integral*. ...*In*29 Cichoń introduce a definition of the*Henstock*-*Kurzweil*delta*integral*HK-Δ*integral**and*HL delta*integral*HL-Δ-*integral*on*Banach**spaces**for*checking the*existence*of solutions of differential or ...##
###
Page 8973 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
*
Mathematical Reviews
*

McKibben (Baltimore, MD)
2002m:34111 34K30 26A39 34A60
Sikorska-Nowak, Aneta (PL-POZNM; Poznan)
Retarded functional differential

*equations**in**Banach**spaces**and**Henstock*-*Kurzweil**integrals*. ... She transcribes the*equation*into*in*- tegral form*and*introduces the HL*integral*, which is the*Kurzweil*-*Henstock**integral*modified*in*such a way that the Saks-*Henstock*lemma is valid (which is not the ...##
###
Page 291 of Mathematical Reviews Vol. , Issue 99a
[page]

1991
*
Mathematical Reviews
*

*integral*

*equation*

*and*the

*Henstock*-

*Kurzweil*

*integral*. ... to quasilinear

*integrodifferential*

*equations*

*in*

*Banach*

*spaces*. ...

##
###
Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces

2016
*
Boundary Value Problems
*

The aim of this paper is to discuss the

doi:10.1186/s13661-016-0716-2
fatcat:tfu24k3dhfellfgmjxppapddhi
*existence*of weak solutions*for*a nonlinear two-point boundary value problem of*integrodifferential**equations*of fractional order α ∈ (1, 2]. ... MSC: 26A39; 35D30; 45B05; 35S15 Keywords: weak solutions;*Henstock*-*Kurzweil*-Pettis*integral*; Caputo fractional derivative; measure of weak noncompactness; boundary value problem c D α + x(t) = f (t, x ... Acknowledgements The authors wish to thank the referees*for*their endeavors*and*valuable comments. This work is supported by National Natural Science Foundation of China (11061031). ...##
###
Page 2484 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

The following modification of the definition of the

*Kurzweil*-*Henstock**integral**for*functions f: R — X is considered: f is K*-*integrable**and*J € X is its K*-*integral*if*for*every « > 0 there*exist*a gauge ... Let R be a compact interval*in*R”*and*X a*Banach**space*. ...##
###
Some Classes of Function Spaces, Their Properties, and Applications

2013
*
Journal of Function Spaces and Applications
*

Méndez et al. contains a few results concerning the completion of the

doi:10.1155/2013/360980
fatcat:wbx74s7dpfhe3i2vfg7ndtwtje
*space*of functions which are*Henstock*-*Kurzweil**integrable*. The authors consider that*space*with the so-called Alexiewicz norm. ...*equations*,*integral**equations*, functional differential, functional*integral**and*functional*equations*, operator*equations*,*and*so forth. ... We hope that the results included*in*this issue will be an inspiration*for*researchers working*in*the*theory*of function*spaces**and*nonlinear analysis. ...##
###
Page 720 of Mathematical Reviews Vol. , Issue Subject Index
[page]

*
Mathematical Reviews
*

2002k:34158
Sikorska-Nowak, Aneta Retarded functional differential

*equations**in**Banach**spaces**and**Henstock*-*Kurzweil**integrals*. ...*Existence*results on infinite intervals*for*neutral functional differential*and**integrodifferential*inclusions*in**Banach**spaces*. ...##
###
Page 737 of Mathematical Reviews Vol. , Issue Subject Index
[page]

*
Mathematical Reviews
*

*Henstock*-

*Kurzweil*

*and*

*Henstock*-

*Kurzweil*-Pettis

*integrals*

*and*some

*existence*theorems. (see 2001d:00033) Domokos, A. ... .) *& Nonlinear differential

*equations*

*in*ordered

*spaces*. 2001e:34112 Chai, Guo Qing (with Hu, Song Lin)

*Existence*

*and*uniqueness of solution of differential

*equations*

*in*

*Banach*

*spaces*. (Chinese. ...

##
###
Page 705 of Mathematical Reviews Vol. 32, Issue Index
[page]

*
Mathematical Reviews
*

*equations*with unbounded delay

*and*

*Henstock*-

*Kurzweil*

*integrals*. ... (English summary) 2000g:39007 Liu, Xinzhi (with Guo, Da Jun) Method of upper

*and*lower solutions

*for*second- order impulsive integro-differential

*equations*

*in*a

*Banach*

*space*. ...

##
###
Page 884 of Mathematical Reviews Vol. 31, Issue Index
[page]

*
Mathematical Reviews
*

*Existence*theorems

*for*fractional set-valued

*integral*

*equations*

*in*

*Banach*

*spaces*. ... (English summary) 994:45007 —

*Existence*of solutions

*for*Volterra

*integral*

*equations*

*in*

*Banach*

*spaces*

*and*monotone iterative techniques. (Chinese. ...

##
###
Page 584 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

On retarded functional- differential

*equations**and**Henstock*-*Kurzweil**integrals*. ... (with Guo, Da Jun) Method of upper*and*lower solutions*for*nonlinear*integrodifferential**equations*of mixed type*in**Banach**spaces*. ...