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The Integrals of Fractional Operators with Non-Singular Kernels: A Conceptual Approach, Formulations, and Normalization Functions |
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PP: 627-662 |
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doi:10.18576/pfda/100409
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Author(s) |
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Jordan Hristov,
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Abstract |
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| Integrals pertinent to fractional operators with non-singular kernels (Caputo-Fabrizio and Atanagana-Baleanu) have been considered and analyzed. Special attention has been paid to the definitions of associate and constitutive integrals, clearly defining the principal differences between them. A conceptual application of the constitutive integrals to the construction of models, applying both the fading memory concept and Volterra equations, has been exemplified by one-dimensional transient heat conduction yielding fractional operators of Caputo-Fabrizio and Atangana-Baleanu in both Caputo and Riemann-Liouville sense. A special focus of the study is the definition and analysis of the normalization functions (M(α) and B(α)) pertinent to these operators, systematically neglected in the literature after the conjecture of Losada and Nieto in 2015, that defining the Caputo-Fabrizio operator M (α ) has to be accepted conventionally equal to unity.
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