DK

Kumar R.

Also known as: Dr. Raj Santosh

Zakir Husain Delhi College, University of Delhi, Kamala Nehru College, Mohanlal Sukhadia University, Central University of Rajasthan, Rajiv Gandhi PG College

ORCID iD 0000-0001-6959-4351
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About

I am currently conducting research on fractional calculus within the framework of bicomplex space. My work involves extending the order of the Riemann-Liouville fractional operator to bicomplex numbers. Initially, this was applied to bicomplex-valued functions of a real variable. Building on this, I generalized the approach to bicomplex-valued functions of bicomplex variables.

My subsequent research focuses on Caputo fractional operators of bicomplex order. In this study, I also consider bicomplex-valued functions of real variables, providing a comparative analysis with the Riemann-Liouville fractional operator in bicomplex space. As an application, I explore the behavior of electric and magnetic fields in electromagnetics, formulating fractional Maxwell-type equations. Solutions to these Maxwell equations are derived using bicomplex vector fields in bicomplex space, facilitated by bicomplex Laplace and inverse Laplace transforms.

Further work delves into the bicomplex Laplace, bicomplex Mellin, and bicomplex Fourier transforms of bicomplex Riemann-Liouville fractional operators. This research addresses various fractional differential equations incorporating these newly defined operators in bicomplex space and their solutions. Additionally, I examine various LCR circuits to highlight the practical applications of my work. My research on the bicomplex Caputo derivative was conducted under a project funded by Rashtriya Uchchatar Shiksh Abhiyan.

Employment

  • Zakir Husain Delhi College, University of Delhi Assistant Professor
    2023 - Present
  • Kamala Nehru College Assistant Professor
    2022 - 2023
  • Rajiv Gandhi PG College Assistant Professor
    2018 - 2019

Education

  • Mohanlal Sukhadia University Ph.D.
    2019 - 2024
  • Central University of Rajasthan M.Sc.
    2015 - 2017

Projects & Funding

Projects & funding information is unavailable.

Publications (19)

  • Bicomplex fractional wave equations
    International Journal of Mathematics for Industry 2025 DOI: 10.1142/S2661335225500157
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  • Bicomplex Caputo Derivative: A Comparative Study with Bicomplex Riemann-Liouville Operators and Applications
    Proceedings of the National Academy of Science India : A Physical Science 2024
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  • Generalization of Riemann-Liouville fractional operators in bicomplex space and applications,
    Mathematics and Statistics 2023
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  • Riemann–Liouville fractional operators of bicomplex order and its properties
    Mathematical Methods in the Applied Sciences 2022 DOI: 10.1002/mma.8135
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  • Bicomplex Laplace Transform of Bicomplex Riemann-Liouville Fractional Operators: Propertier and Implications
    Journal of Rajasthan Academy of Physical Sciences 2022
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  • Bicomplex Fourier Transform of bicomplex Riemann-Liouville Fractional Operators and It’s Properties
    2022
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  • Riemann-Liouville fractional operators of bicomplex order for functions of bicomplex variables and applications
    The 4th International Conference on Mathematical Modelling, Applied Analysis and Computation-2021 (ICMMAAC-21) (A virtual conference) 2021
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  • Riemann-Liouville fractional operators of bicomplex order and its properties
    Riemann-Liouville fractional operators of bicomplex order and its propertiesInternational Virtual Conference on Recent Applications of Mathematical Sciences (RAMS-2021) 2021
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  • Riemann-Liouville Fractional Operators of Bicomplex Order and Its Properties.
    2021 DOI: 10.22541/au.162168235.55847593/v1
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  • Ramanujan Mathematical Society
    35th Annual Conference of the Ramanujan Mathematical Society 2020
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