Baleanu, DumitruOdibat, Zaid2022-10-062025-09-182022-10-062025-09-182021Odibat, Zaid; Baleanu, Dumitru (2021). "On a new modification of the erdélyi–kober fractional derivative", Fractal and Fractional, Vol. 5, No. 3.2504-3110https://doi.org/10.3390/fractalfract5030121https://hdl.handle.net/20.500.12416/10477Odibat, Zaid/0000-0002-2414-7969In this paper, we introduce a new Caputo-type modification of the Erdelyi-Kober fractional derivative. We pay attention to how to formulate representations of Erdelyi-Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdelyi-Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputo-type Erdelyi-Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models.eninfo:eu-repo/semantics/openAccessFractional Integrals And DerivativesRiemann-Liouville Fractional OperatorCaputo Fractional OperatorErdelyi-Kober Fractional OperatorPredictor-Corrector MethodArticle10.3390/fractalfract50301212-s2.0-85115182246