abstract
- In this work, the fractional Schrödinger equation with a specific potential V(x)=0 is analyzed using both Caputo and Caputo-Fabrizio fractional derivatives. The order of the derivative considered is 0<¿¿1 for the Caputo derivative and 0¿¿¿1 for the Caputo-Fabrizio derivative. To address dimensional consistency, the equation was non-dimensionalized, and solutions were obtained in terms of the Mittag-Leffler function. In both cases, the conventional solutions are recovered when ¿=1 , demonstrating consistency with the classical Schrödinger equation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.