Abstract
In this paper, an analog of the conformable fractional derivative is defined in an arbitrary finite-dimensional commutative associative algebra. Functions taking values in the indicated algebras and having derivatives in the sense of a conformable fractional derivative are called φ-monogenic. A relation between the concepts of φ-monogenic and monogenic functions in such algebras has been established. Two new definitions have been proposed for the fractional derivative of the functions with values in finite-dimensional commutative associative algebras.
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Presented by V. Gutlyanskyĭ
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 20, No. 2, pp. 269–282, April–June, 2023.
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Shpakivskyi, V.S. Conformable fractional derivative in commutative algebras. J Math Sci 274, 392–402 (2023). https://doi.org/10.1007/s10958-023-06608-6
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DOI: https://doi.org/10.1007/s10958-023-06608-6