Boundary value problem of Riemann-Liouville fractional differential equations in the variable exponent Lebesgue spaces Lp(.) - Refice, Ahmed; İnç, Mustafa; Hashemi, Mir Sajjad; Souid, Mohammed Said (Elsevier, 2022)
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. (c) 2022 Elsevier B.V. All rights reserved.
Keywords: Fractional differential equations; Boundary value problem; Fixed point theorem; Variable exponent Lebesgue spaces; Banach contraction principle; Ulam-Hyers stability