Baleanu, DumitruOdibat, ZaidBaleanu, Dumitru2022-10-062022-10-062021Odibat, Zaid; Baleanu, Dumitru (2021). "On a new modification of the erdélyi–kober fractional derivative", Fractal and Fractional, Vol. 5, No. 3.2504-3110https://hdl.handle.net/20.500.12416/5804In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdélyi–Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputotype Erdélyi–Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models.eninfo:eu-repo/semantics/openAccessCaputo Fractional OperatorErdélyi–Kober Fractional OperatorFractional Integrals and DerivativesPredictor–Corrector MethodRiemann–Liouville Fractional OperatorArticle5310.3390/fractalfract5030121