Al-Shdaifat, HamzaRodríguez López, Rosana2025-10-172025-10-172025-08-15References Al-Shdaifat, H., & Rodríguez-López, R. (2025). Non-convolutional general fractional operators and some of their properties. Journal of Computational and Applied Mathematics, 464, 116527. 10.1016/j.cam.2025.1165270377-0427https://hdl.handle.net/10347/43134In this work, we propose a general framework for fractional integrals without following a convolution-kernel approach, and consider the corresponding notions for fractional derivatives under different perspectives (Riemann–Liouville and Caputo-type), analyzing their main mathematical properties such as semi-group condition, and the linearity of the integral, as well as the first theorem of calculus. We study some connections between the different notions, and provide a generalized Sonin condition.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Generalized fractional integralGeneralized fractional derivativeNon-convolution kerneljournal article10.1016/j.cam.2025.1165271879-1778open access