期刊
FRACTAL AND FRACTIONAL
卷 5, 期 3, 页码 -出版社
MDPI
DOI: 10.3390/fractalfract5030121
关键词
fractional integrals and derivatives; Riemann-Liouville fractional operator; Caputo fractional operator; Erdelyi-Kober fractional operator; predictor-corrector method
The paper introduces a new Caputo-type modification of the Erdelyi-Kober fractional derivative, focusing on representations, properties, and relationships with other fractional derivatives. A numerical method is presented to deal with fractional differential equations involving the proposed modification, with the hope of widespread application in simulating fractional models.
In 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.
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