Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space

Abstract

In this article, we establish a new tempered sequence space related to tempered sequence $$\ell _{p}^{\alpha },$$ $$p\ge 1$$ and obtain the Hausdorff measure of noncompactness of this space. By using this measure of noncompactness with Darbo’s fixed point theorem, we investigate the existence results for an infinite system of Langevin fractional differential equations involving a generalized derivative of two distinct fractional orders with three-point boundary conditions in this new sequence space. To illustrate the obtained results of these sequence spaces, a numerical example is provided.