Riemann–Liouville fractional operators of bicomplex order and its properties

Riemann–Liouville fractional operators of bicomplex order and its properties

In this paper, we construct the Riemann–Liouville fractional integral and differential operator of bicomplex order and illustrate some examples to calculate the fractional integration and differentiation of bicomplex order of some elementary bicomplex‐valued functions. Also, we discuss some properti...

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Veröffentlicht in:Mathematical methods in the applied sciences 2022-07, Vol.45 (10), p.5699-5720
Hauptverfasser: Goswami, Mahesh Puri, Kumar, Raj
Format: Artikel
Sprache:eng
Schlagworte:
bicomplex gamma and beta functions
bicomplex numbers
Differential equations
Fractional calculus
idempotent representation
Mathematical analysis
Operators (mathematics)
Riemann–Liouville operators
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Zusammenfassung:In this paper, we construct the Riemann–Liouville fractional integral and differential operator of bicomplex order and illustrate some examples to calculate the fractional integration and differentiation of bicomplex order of some elementary bicomplex‐valued functions. Also, we discuss some properties of these operators by proving analogues of the semigroup property, Leibniz rule, chain rule, etc.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8135