Mathematics and Statistics Vol. 11(5), pp. 802 - 815
DOI: 10.13189/ms.2023.110506
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Generalization of Riemann-Liouville Fractional Operators in Bicomplex Space and Applications

Mahesh Puri Goswami ^1,*, Raj Kumar ^1,2
1 Department of Mathematics and Statistics, Mohanlal Sukhadia University, India
² Zakir Husain Delhi College, University of Delhi, Jawaharlal Nehru Marg, India

ABSTRACT

In this article, we generalize the Riemann-Liouville fractional differential and integral operators that can be applied to the functions of a bicomplex variable. For this purpose, we consider the bicomplex Cauchy integral formula and some contours in bicomplex space. We elaborate these operators through some examples. Also, we contemplate some significant properties of these operators which include a discussion of bicomplex analytical behavior of generalized bicomplex functions through Pochhammer contours, the law of exponents, generalized Leibniz rule along with a depiction of the region of convergence, and generalized chain rule for Riemann-Liouville fractional operators of bicomplex order. We give an application of our work in the construction of fractional Maxwell's type equations in vacuum and sourcefree domains equipped with the Riemann-Liouville derivative operator. For this, we define bicomplex grad, div, and curl operator with the help of these newly defined operators. The advantage of this fractional construction of Maxwell's equation is that it may be used to build fractional non-local electronics in bicomplex space. By considering bicomplex vector fields for the respective domains, we reduce the number of these fractional Maxwell's type equations by half, which makes it easier to extract electric and magnetic fields from the bicomplex vector fields.

KEYWORDS
Idempotent Representation, Bicomplex Gamma and Beta Functions, Functions of Bicomplex Variable, Riemann-Liouville Operators of Bicomplex Order

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mahesh Puri Goswami , Raj Kumar , "Generalization of Riemann-Liouville Fractional Operators in Bicomplex Space and Applications," Mathematics and Statistics, Vol. 11, No. 5, pp. 802 - 815, 2023. DOI: 10.13189/ms.2023.110506.

(b). APA Format:
Mahesh Puri Goswami , Raj Kumar (2023). Generalization of Riemann-Liouville Fractional Operators in Bicomplex Space and Applications. Mathematics and Statistics, 11(5), 802 - 815. DOI: 10.13189/ms.2023.110506.