Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

Ravi P Agarwal,Donal O’Regan,Vasile Lupulescu,Ghaus Ur Rahman

doi:10.1186/s13662-015-0451-5

Abstract

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1):59-73, 2015; Adv. Differ. Equ. 2013:302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces.

Highlights

One of the sections, Section, of our paper [ ] contains a number of ambiguities which we correct here
Let Cw(T, E) denote the space of all weakly continuous functions from T into Ew endowed with the topology of weak uniform convergence
If y(·) : T → E is a pseudo-differentiable function on T with a pseudo-derivative x(·) ∈ P∞(T, E), the fractional Pettis integral I –αx(t) exists on T

Summary

Introduction

Section , of our paper [ ] contains a number of ambiguities (and inaccuracies) which we correct here. Let Cw(T, E) denote the space of all weakly continuous functions from T into Ew endowed with the topology of weak uniform convergence.

Objectives

Results

Conclusion