[6] viXra:1810.0313 [pdf] submitted on 2018-10-19 06:28:06
Authors: Fayowole David Ayadi
Comments: 3 Pages.
Abstract:I can still remember my expression and feeling when we were asked to show that sup(A + B) = sup(A) + sup(B). It was an herculean task because the concept was too difficult to grasp with the use of approximation property until I discovered an easy route. In a bid to restrict my papers to just few pages, I will focus more on examples than theorems.
Category: Functions and Analysis
[5] viXra:1810.0312 [pdf] submitted on 2018-10-19 06:32:53
Authors: Fayowole David Ayadi, Olabiyi Tobi David, Oluwajoba Godsfavour Favour, Oluwusi Faith Tolu, Isaleye Dorcas, Olorunisola Femi Stephen
Comments: 13 Pages.
Throughout these discussions the numbers epsilon > 0 and delta > 0 should be thought of as very small numbers. The aim of this part is to provide a working definition for the integral of a bounded function f(x) on the interval [a, b]. We will see that the real number "f(x)dx" is really the limit of sums of areas of rectangles.
Category: Functions and Analysis
[4] viXra:1810.0308 [pdf] replaced on 2019-04-04 22:58:32
Authors: Zaid Laadjal
Comments: 4 Pages.
In this work, we apply the fixed point theorems, we study the existence and uniqueness of solutions for Langevin differential equations involving two ractional orders with multi-point boundary conditions on the half-line.
Category: Functions and Analysis
[3] viXra:1810.0170 [pdf] submitted on 2018-10-10 15:15:29
Authors: Zaid Laadjal
Comments: 4 Pages.
In this paper, we study the existence and uniqueness of solutions for Langevin differential equations of Riemman-Liouville fractional derivative with boundary value conditions on the half-line. By a classical fixed point theorems, several new existence results of solutions are obtained.
Category: Functions and Analysis
[2] viXra:1810.0169 [pdf] submitted on 2018-10-10 15:21:57
Authors: Zaid Laadjal
Comments: 5 Pages.
In this paper, we investigate the existence and uniqueness of solutions for the following fractional Langevin equations with boundary conditions $$\left\{\begin{array}{l}D^{\alpha}( D^{\beta}+\lambda)u(t)=f(t,u(t)),\text{ \ \ \ }t\in(0,+\infty),\\ \\u(0)=D^{\beta}u(0)=0,\\ \\ \underset{t\rightarrow+\infty}{\lim}D^{\alpha-1}u(t)=\underset{t\rightarrow+\infty}{\lim}D^{\alpha +\beta-1}u(t)=au(\xi),\end{array}\right.$$ where $1<\alpha \leq2$ and$\ 0<\beta \leq1,$ such that $1<\alpha +\beta \leq2,$ with $\ a,b\in\mathbb{R},$ $\xi \in\mathbb{R}^{+},$\ and $D^{\alpha}$, $D^{\beta }$ are the Riemman-Liouville fractional derivative. Some new results are obtained by applying standard fixed point theorems.
Category: Functions and Analysis
[1] viXra:1810.0168 [pdf] submitted on 2018-10-10 15:28:53
Authors: Zaid Laadjal
Comments: 6 Pages.
In this work, we use the fixed point theorems, we investigate the existence and uniqueness of solutions for a class of fractional Langevin equations with boundary value conditions on an infinite interval.
Category: Functions and Analysis