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

Abstract

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 . We convert the variable exponent Lebesgue spaces 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.