In this paper, we propose a new integrable fractional Fokas--Lenells equation
by using the completeness of the squared eigenfunctions, dispersion relation,
and inverse scattering transform. To solve this equation, we employ the
Riemann-Hilbert approach. Specifically, we focus on the case of the
reflectionless potential with a simple pole for the zero boundary condition.
And we provide the fractional N-soliton solution in determinant form.
Additionally, we prove the fractional one-soliton solution rigorously. Notably,
we demonstrate that as β£tβ£ββ, the fractional N-soliton solution can
be expressed as a linear combination of N fractional single-soliton
solutions