This manuscript deals with the existence, uniqueness and stability of solutions to the boundary value problem (BVP) of Riemann-Liouville (RL) fractional differential equations (FDEs) in the variable exponent Lebesgue spaces (Lp(.)). The generalized intervals and piece-wise constant functions are utilized to extract the aims of current paper. The variable exponent Lebesgue spaces (Lp(.)) are converted to the classical Lebesgue spaces. Further, the Banach contraction principle is used, the Ulam-Hyers-stability is examined and finally, an illustrative example is given to the validity of the observed results.
