Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2011
Volume
Vol. 31
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 31 (2011)
Projects
Pages
Articles
Investigating the numerical range and q-numerical range of non square matrices
(2011) Aretaki, Aikaterini; Maroulas, John
A presentation of numerical ranges for rectangular matrices is undertaken in this paper, introducing two different definitions and elaborating basic properties. Further, we extend to the $q$-numerical range.
Stability of the Popoviciu type functional equations on groups
(2011) Chudziak, Małgorzata
We consider the stability problem for a class of functional equations related to the Popoviciu equation.
Monotone iterative technique for finite systems of nonlinear Riemann-Lliouville fractional differential equations
(2011) Denton, Z.; Vatsala, A. S.
Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order $q$, $0 \lt q \leq 1$, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order $q$, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.
On nonlocal problems for fractional differential equations in Banach spaces
(2011) Dong, XiWang; Wang, JinRong; Zhou, Yong
In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
(2011) Dou, Xiaoyan; Li, Yongkun; Liu, Ping
In this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for the problem by using the Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered to the equivalent Fredholm integral equation.