In this paper, we propose a new nonlinear Langevin equation of fractional orders with nonlocal boundary value conditions which is a generalization of previous Langevin equations. By applying some fixed point theorems such as Schauder and contraction mapping principle, the existence and uniqueness of solutions are studied. An example to illustrate our results is given.
In this paper, we first introduce the concept of fractional quantum integral with general kernels, which generalizes several types of fractional integrals known from the literature. Then we give more general versions of some integral inequalities for this operator, thus generalizing some previous results obtained by many researchers.2,8,25,29,30,36
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