# Functions and Analysis

## 1810 Submissions

[3] **viXra:1810.0170 [pdf]**
*submitted on 2018-10-10 15:15:29*

### Existence of Solutions for Langevin Differential Equations Involving Two Fractional Orders on the Half-Line

**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*

### Existence of Solutions for Fractional Langevin Equations with Boundary Conditions on an Infinite Interval

**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*

### Existence of Solutions for a Class of Nonlinear Fractional Langevin Equations with Boundary Conditions on the Half-Line

**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