Terminal value problem for Riemann-Liouville fractional differential equation in the variable exponent Lebesgue space Lp(.)$$ {L}boolean AND{p(.)} $$

In this manuscript, the existence, uniqueness, and stability of solutions to the terminal value problem of Riemann-Liouville fractional equations are established in the variable exponent Lebesgue spaces L-p(.). We convert the variable exponent Lebesgue spaces L-p(.) to the Lebesgue spaces using the generalized intervals and piece-wise constant function. Further, the Banach contraction principle is used, the Ulam-Hyers-stability is examined, and finally, we construct an example.