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In this paper, we study the existence and uniqueness of nonnegative solutions of an initial value problem for Langevin equations involving two fractional orders: $$\begin{aligned} \left\{ \begin{array}{lll}^c_0\!D^\beta _t({}^c_0\!D^\alpha _t-\gamma )x(t)=f(t,x(t)),&{}\quad… Click to show full abstract
In this paper, we study the existence and uniqueness of nonnegative solutions of an initial value problem for Langevin equations involving two fractional orders: $$\begin{aligned} \left\{ \begin{array}{lll}^c_0\!D^\beta _t({}^c_0\!D^\alpha _t-\gamma )x(t)=f(t,x(t)),&{}\quad \ 0< t<1,\\ x^{(k)}(0)=\mu _k,&{}\quad \ 0\le k
Keywords:
solutions initial;
initial value;
nonnegative solutions;
langevin equations;
alpha;
equations involving
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2018
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Journal Title: Mediterranean Journal of Mathematics
Year Published: 2018
Link to full text (if available)
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recommendations!