Person:
Sharma, Madhukant

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Madhukant Sharma

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Faculty

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079-68261554

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Fractional Differential Equations (FDEs), Optimization, Numerical Methods for FDEs, Signal Processing

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Biography

Dr. Madhu Kant Sharma received his M.Sc. (Mathematics) degree (2008-2010) from the Indian Institute of Technology Kanpur and his Ph.D. degree in Mathematics (2011-2015) from the Indian Institute of Technology Madras. He has held academic positions as an Assistant Professor at the Mahindra Ecole Centrale Hyderabad (Aug. 2015 � Jul. 2018) and at the Indian Institute of Information Technology Dharwad (Aug. 2018 � May 2020). From June 2020 to April 2025, he was an Assistant Professor at the Dhirubhai Ambani Institute of Information and Communication Technology (DA-IICT) in Gandhinagar. Since May 2025, he has been serving�as an Associate Professor at DA-IICT.�His current research interests include the analytical and numerical study of Fractional Differential Equations (FDEs), Applications of FDEs, Optimization Techniques, and Signal Processing.

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2021 - 20245

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Now showing 1 - 5 of 5
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    Solvability and Controllability of a Retarded-Type Nonlocal Non-Autonomous Fractional Differential Equation
    (Natural Science Publishing, 01-07-2023) Sharma, Madhukant; Dubey, Shruti; DA-IICT, Gandhinagar
    This paper considers a non-autonomous retarded-type fractional differential equation involving Caputo derivative along with a nonlocal condition in a general Banach space. We present a novel approach to determine the existence-uniqueness and controllability of mild solution to the considered problem using the fixed-point technique, classical semigroup theory, and tools of fractional calculus. It is imperative to mention that the main results are established without assuming the continuity of linear operator ?A(t) and compactness condition on semigroup. At the end, the developed theoretical results have been applied to a nonlocal fractional order retarded elliptic evolution equation.
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    Existence of optimal pairs and solvability of non-autonomous fractional Sobolev-type integrodifferential equations
    (Springer, 04-07-2023) Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; DA-IICT, Gandhinagar
    This article establishes a sufficient criteria for the existence of an optimal pair and a mild-solution of a non-autonomous fractional Sobolev-type integro-differential equation (FSIDE) with a generalized nonlocal condition. The fixed-point technique, tools from fractional calculus and the semigroup-theory played a valuable role in deriving the results. It is imperative to mention the distinguish attributes of this work that the developed results don�t assume (i) that the generated semigroup is compact; (ii) that the linear operators��are bounded; and (iii) that the operator�D�is strongly continuous. We also provide an example to demonstrate the established results.
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    MGDMD: Multi-variate generalized dispersive mode decomposition
    (Elsevier, 01-07-2022) Sharma, Madhukant; Satija, Udit; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; DA-IICT, Gandhinagar
    In this paper, we propose a multi-variate extension of the recently proposed generalized dispersive mode decomposition (GDMD) which can accurately estimate cross group delays and extract overlapped dispersive modes. We propose a joint dispersion optimization solution for multi-channel dispersive signals which can extract all high-quality overlapped dispersive modes with very few cross dispersion effects. Simulation results on multi-channel synthetic dispersive signals and real-life signals taken from four publicly available datasets depict the superiority of the proposed multi-variate GDMD (MGDMD) as compared to existing decomposition techniques.
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    A Robust Higher-Order Scheme for Fractional Delay Differential Equations Involving Caputo Derivative
    (Springer, 22-08-2024) Prusty, Biswajit; Sharma, Madhukant; DA-IICT, Gandhinagar; Prusty, Biswajit (201921007)
    This article considers nonlinear fractional delay differential equations involving Caputo�s fractional derivative of order�. We focus on designing a robust numerical algorithm of order�. To achieve this, we developed a higher-order interpolation-based approximation for Caputo�s derivative, which enables us to construct a robust numerical scheme for the considered problem. Furthermore, we discuss the stability and error analysis of the proposed higher-order scheme. Finally, numerous examples, including real-life applications, are evaluated to demonstrate the computational efficiency of the proposed algorithm.
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    Solvability and Optimal Control of Nonautonomous Fractional Dynamical Systems of Neutral-Type with Nonlocal Conditions
    (Springer, 15-09-2021) Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; Sharma, Madhukant; DA-IICT, Gandhinagar
    This paper discusses the solvability and existence of optimal controls of nonautonomous fractional dynamical systems of neutral-type in a general Banach space�X�along with nonlocal condition. We employ the Banach contraction principle, the classical semigroup theory, and the techniques of fractional calculus to establish the main results. The distinguish features of the presented work are that we establish the main results without imposing the compactness condition on semigroup, the continuity of linear operators��and the strong continuity of operator�D. At the end, an example is considered to demonstrate the developed results.