THANGARAJ C

@vignan.ac.in

Assistant Professor
Vignan Foundation for Science, Technology and Research

THANGARAJ C


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https://researchid.co/ctrmath1
C. Thangaraj received a Bachelor of Science in Mathematics from Arignar Anna College, Krishnagiri, Tamil Nadu in 2011, and a Master of Science in Mathematics from Bharathidasan University, Tiruchirappalli, Tamil Nadu in 2014. He was completed his doctoral program in Mathematics at Vellore Institute of Technology, Vellore, Tamil Nadu, India in 2023. His areas of research are fractal analysis, fixed point theory, iterated function systems, and multifractal analysis on image processing. Now currently working in Assistant Professor at Vignan's Foundation for Science, Technology and Research.

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics, Analysis, Applied Mathematics, Geometry and Topology
17

Scopus Publications

115

Scholar Citations

7

Scholar h-index

4

Scholar i10-index

Scopus Publications

  • Nonlocal Fractal Diffusion-Advection Models with Variable Coefficients and Nonlocal Time Delay: Existence of Solutions, Lyapunov Function, Hopf Bifurcation, and Stability
    Rami Ahmad El-Nabulsi, Waranont Anukool, Raja Valarmathi, Chinnasamy Thangaraj
    Journal of Peridynamics and Nonlocal Modeling, 2026
  • A unified fractional action integral framework for memory-dependent circuit dynamics and Josephson junctions
    Rami Ahmad El-Nabulsi, Waranont Anukool, Raja Valarmathi, Chinnasamy Thangaraj
    Journal of Electronic Science and Technology, 2026
    This study presents a unified framework for analyzing electric circuits and Josephson junctions using a fractional action integral that incorporates memory effects and nonlocal behavior. Unlike classical integer-order models, the method extends the action principle to fractional orders, leading to fractional Euler-Lagrange equations that better describe currents, voltages, and phase evolution. It is particularly effective for Josephson junctions, where tunneling currents and phase dynamics show long-term correlations and dissipation. By including fractional-order elements, the framework captures anomalous damping, power-law relaxation, and persistent memory effects in complex circuits. Using a dissipative fractional standard map, the study investigates chaos and the influence of memory on system stability. Numerical results reveal strong sensitivity to fractional parameters, including bifurcations and chaotic attractors. These findings link the classical circuit theory with fractional dynamics, offering new insights for superconducting electronics and the design of nonlinear systems.
  • Fractal Laplacian approach to quantum wave localization
    Raja Valarmathi, Chinnasamy Thangaraj, Rami Ahmad El-Nabulsi, Waranont Anukool
    Modern Physics Letters A, 2026
    The traditional Schrödinger equation is expressed in smooth Euclidean space, wherein the Laplacian operator embodies integer-dimensional geometry. Nonetheless, some natural and quantum systems have irregular, self-similar structures that are more accurately described by non-integer, or fractal, dimensions. This study presents a theoretical enhancement of the Schrödinger equation by the introduction of a fractal Laplacian operator defined over a domain of fractal dimension [Formula: see text]. The new operator takes into consideration scale invariance and non-integer spatial dimensions, which makes it possible to rewrite the kinetic term in terms of fractal scaling. Analytical derivation shows that the energy eigenvalues scale as [Formula: see text], which is not the same as the normal [Formula: see text] dependence seen in integer dimensions. The requirement for normalization is restated by employing integration over a fractal measure. This paradigm offers a purely mathematical basis for the examination of quantum behavior on fractal geometries, connecting spectral theory with fractal analysis without relying on any physical or experimental premises.
  • Extended spin-orbit modeling of unstable discrete fractional Hamiltonian systems: numerical investigation of chaotic orbits for Mercury, Mars, Triton, and Sedna-like trans-Neptunian objects
    Rami Ahmad El-Nabulsi, Waranont Anukool, Raja Valarmathi, Chinnasamy Thangaraj
    Advances in Space Research, 2026
  • RGB Image Edge Detection Using Fuzzy Inference Techniques
    T. L. Yookesh, M. Loganathan, C. Thangaraj, E. Boopathi Kumar
    Aip Conference Proceedings, 2026
  • Acceleration-dependent hamiltonian for the zeros of the riemann zeta function: Spectral properties and self-adjoint realizations of the new operator
    Waranont Anukool, Rami Ahmad El-Nabulsi, Raja Valarmathi, Chinnasamy Thangaraj
    Modern Physics Letters A, 2026
    An acceleration-dependent Hamiltonian operator [Formula: see text] and its corresponding Hamiltonian operator [Formula: see text] are introduced based on the new notion of quantum acceleratum operator. The new Hamiltonian operator consists of two independent parts: the Berry–Keating (BK) operator [Formula: see text] and the new operator part [Formula: see text] which depends on the acceleratum operator [Formula: see text]. The Hamiltonian [Formula: see text] offers new features for the zeros of the Riemann zeta function. The operator couples [Formula: see text] with a higher-order interaction involving the position and acceleratum operators, introducing nonlinear effects beyond conventional canonical mechanics. The structure of this coupling determines whether the eigenvalue spectrum remains discrete or transitions to a continuous regime, reflecting the balance between confinement and scaling symmetry. Establishing conditions for spectral discreteness provides key insight into the existence of bound states, the boundedness of energy levels, and the physical realizability of acceleration-dependent quantum dynamics. Such analysis extends the mathematical framework of self-adjoint operators and spectral theory to higher-order Hamiltonians, offering new perspectives on quantization in extended phase-space formulations and on the emergence of discrete energy spectra in nonstandard dynamical systems.
  • Stability and chaos in nonstandard Hamiltonian planetary dynamics
    Rami Ahmad El-Nabulsi, Waranont Anukool, Chinnasamy Thangaraj, Raja Valarmathi
    Chaos Solitons and Fractals, 2026
  • Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems
    Rami Ahmad El-Nabulsi, Chinnasamy Thangaraj, Raja Valarmathi, Waranont Anukool
    Chaos Solitons and Fractals, 2025
  • Fractal based automatic detection of complexity in COVID-19 X-ray images
    C. Thangaraj, D. Easwaramoorthy, G. Muhiuddin, Bilel Selmi, Vladimir Kulish
    Expert Systems, 2025
    The coronavirus was discovered in Wuhan, China, in December 2019. Scientists and medical practitioners have warned that this fatal virus could spread quickly from person to person in its early stages and its impact will be far more vigorous than the previously discovered viruses. The World Health Organization has given warning propaganda to all nations about this harmful virus. However, the diffusion speed of COVID‐19 was so rapid that it spread to all countries much faster than the researchers predicted, causing the widespread human disaster. The genetic variations of COVID‐19 have also astounded researchers today, as it modifies its mutation with very large genetic strains. The virus is regarded as a human version of the disease, resulting in the common cold, dry cough, and respiratory problems in severe cases. According to health organisations, the coronavirus directly affects the lungs, causing main problems such as difficulty breathing. It is also tough for physicians to diagnose the disease level properly by using the regular process. Even though the virus can be detected in regular testing methods, even computed tomography (CT) and X‐ray images are widely used in the medical field to identify the respiratory problems caused by the COVID‐19 virus. Like COVID‐19, some other types of pneumonia respiratory diseases also affect the human lungs. The fractal dimension (FD) is an interesting non‐linear measure to describe the complexity of visual images. In this context, the complexity of X‐ray images is analysed by using the fractal dimension. The fractal dimension is an excellent non‐linear measurement for describing the complexity of realistic images. The difference between the complexity of the X‐ray images of COVID‐19‐infected patients and the X‐ray images of other types of pneumonia respiratory diseases is well explained by using the fractal dimension. It is also concluded that the fractal dimension discriminates the lung diseases due to COVID‐19 from various pneumonia respiratory diseases.
  • Multifractal Analysis in Age-Based Classi¯cation for COVID-19 Patients' CT-Scan Images with Di®erent Noise Levels
    R. Valarmathi, C. Thangaraj, D. Easwaramoorthy, Bilel Selmi, Hajer Jebali, Christo Ananth
    Fluctuation and Noise Letters, 2024
    Recently, many number of people various countries contracted the COVID-19 (C-19) disease. The identification of this harmful disease and other pneumonia diseases is an important process in the medical world. CT-Scan is mainly prescribed to predict the severity of lung diseases affected by C-19 and other pneumonia diseases. Generally, a CT-Scan image is represented as a grayscale image (GI). Biomedical-oriented GIs are more complex and they are too difficult to recognize the status of lung diseases directly from the experimental images. To address this type of medical problem, a multifractal approach can be applied to analyze and illustrate the GIs in detail. Therefore, the multifractal dimensional analysis is used to diagnose and explore the vehemence of the contamination levels in the lungs. In this study, the complexity of CT-Scan images of C-19 patients is analyzed in order to perform a comparison in terms of age and noise levels. It was also discovered that the intricate of CT-Scan images is considerably varied for patients aged 50 and above when compared to younger subjects. This comparative study indicates that the deadly virus affects elderly persons compared to youngsters. The proposed age-based classification is supported by image processing techniques, qualitative measures, and statistical tools. The obtained results are demonstrated graphically by Generalized Fractal Dimensions (GFD) spectrum, 3D visualization, ANOVA table, and box plots to expose the rate of discrimination of complexity in CT-Scan lung images.
  • Generation of fractals via iterated function system of Kannan contractions in controlled metric space
    C. Thangaraj, D. Easwaramoorthy, Bilel Selmi, Bhagwati Prasad Chamola
    Mathematics and Computers in Simulation, 2024
  • Fractals via Self-Similar Group of Fisher Contractions
    C. Thangaraj, D. Easwaramoorthy
    Trends in Mathematics, 2024
  • Generation of Fractal Attractor for Controlled Metric Based Dynamical Systems
    C. Thangaraj, R. Valarmathi, D. Easwaramoorthy, D. Ramesh Kumar, Bhagwati Prasad Chamola
    Contemporary Mathematics Singapore, 2024
  • Fractals via Controlled Fisher Iterated Function System
    C. Thangaraj, D. Easwaramoorthy
    Fractal and Fractional, 2022
  • Generalized fractal dimensions based comparison analysis of edge detection methods in CT images for estimating the infection of COVID-19 disease
    C. Thangaraj, D. Easwaramoorthy
    European Physical Journal Special Topics, 2022
  • Multifractal analysis on age-based discrimination in X-ray images for sensing the severity of COVID-19 disease
    Shaobo He, C. Thangaraj, D. Easwaramoorthy, G. Muhiuddin
    European Physical Journal Special Topics, 2022
  • Multifractal based image processing for estimating the complexity of COVID-19 dynamics
    Qiusheng Rong, C. Thangaraj, D. Easwaramoorthy, Shaobo He
    European Physical Journal Special Topics, 2021

RECENT SCHOLAR PUBLICATIONS

  • Nonlocal Fractal Diffusion-Advection Models with Variable Coefficients and Nonlocal Time Delay: Existence of Solutions, Lyapunov Function, Hopf Bifurcation, and Stability
    RA El-Nabulsi, W Anukool, R Valarmathi, C Thangaraj
    Journal of Peridynamics and Nonlocal Modeling 8 (1), 6 , 2026
    2026
  • A unified fractional action integral framework for memory-dependent circuit dynamics and Josephson junctions
    RA El-Nabulsi, W Anukool, R Valarmathi, C Thangaraj
    Journal of Electronic Science and Technology, 100362 , 2026
    2026
  • Fractal Laplacian approach to quantum wave localization
    R Valarmathi, C Thangaraj, RA El-Nabulsi, W Anukool
    Modern Physics Letters A 41 (11), 2650047 , 2026
    2026
  • RGB image edge detection using fuzzy inference techniques
    TL Yookesh, M Loganathan, C Thangaraj, EB Kumar
    AIP Conference Proceedings 3348 (1), 020009 , 2026
    2026
  • Extended Spin-Orbit Modeling of Unstable Discrete Fractional Hamiltonian Systems: Numerical Investigation of Chaotic Orbits for Mercury, Mars, Triton, and Sedna-like Trans …
    RA El-Nabulsi, W Anukool, R Valarmathi, C Thangaraj
    Advances in Space Research , 2026
    2026
    Citations: 1
  • Acceleration-dependent hamiltonian for the zeros of the riemann zeta function: Spectral properties and self-adjoint realizations of the new operator
    W Anukool, RA El-Nabulsi, R Valarmathi, C Thangaraj
    Modern Physics Letters A 41 (01), 2550219 , 2026
    2026
  • Stability and chaos in nonstandard Hamiltonian planetary dynamics
    RA El-Nabulsi, W Anukool, C Thangaraj, R Valarmathi
    Chaos, Solitons & Fractals 202, 117410 , 2026
    2026
    Citations: 3
  • Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems
    RA El-Nabulsi, C Thangaraj, R Valarmathi, W Anukool
    Chaos, Solitons & Fractals 200, 116974 , 2025
    2025
    Citations: 7
  • Fractal based automatic detection of complexity in COVID‐19 X‐ray images
    C Thangaraj, D Easwaramoorthy, G Muhiuddin, B Selmi, V Kulish
    Expert Systems 42 (1), e13497 , 2025
    2025
    Citations: 8
  • Multifractal analysis in age-based classification for COVID-19 patients’ CT-scan images with different noise levels
    R Valarmathi, C Thangaraj, D Easwaramoorthy, B Selmi, H Jebali, ...
    Fluctuation and Noise Letters 23 (05), 2440055 , 2024
    2024
    Citations: 12
  • Generation of fractals via iterated function system of Kannan contractions in controlled metric space
    C Thangaraj, D Easwaramoorthy, B Selmi, BP Chamola
    Mathematics and Computers in Simulation 222, 188-198 , 2024
    2024
    Citations: 34
  • Fractals via Self-Similar Group of Fisher
    C Thangaraj, D Easwaramoorthy
    Recent Developments in Algebra and Analysis: International Conference on … , 2024
    2024
  • Generation of Fractal Attractor for Controlled Metric Based Dynamical Systems
    C Thangaraj, R Valarmathi, D Easwaramoorthy, DR Kumar, B Prasad
    Contemporary Mathematics 5 (Issue 4), 6165 , 2024
    2024
    Citations: 1
  • Fractals via controlled fisher iterated function system
    C Thangaraj, D Easwaramoorthy
    Fractal and Fractional 6 (12), 746 , 2022
    2022
    Citations: 5
  • Generalized fractal dimensions based comparison analysis of edge detection methods in CT images for estimating the infection of COVID-19 disease
    C Thangaraj, D Easwaramoorthy
    The European Physical Journal Special Topics 231 (18), 3717-3739 , 2022
    2022
    Citations: 18
  • Multifractal analysis on age-based discrimination in X-ray images for sensing the severity of COVID-19 disease
    S He, C Thangaraj, D Easwaramoorthy, G Muhiuddin
    The European Physical Journal Special Topics 231 (18), 3663-3671 , 2022
    2022
    Citations: 9
  • Fractals via Self-Similar Group of Fisher Contractions
    C Thangaraj, D Easwaramoorthy
    International Conference on Recent Developments in Mathematics, 347-356 , 2022
    2022
    Citations: 1
  • Multifractal dimensions and fractional differentiation in automated edge detection on intuitionistic fuzzy enhanced image
    VP Ananthi, C Thangaraj, D Easwaramoorthy
    Frontiers of Fractal Analysis, 153-171 , 2022
    2022
    Citations: 1
  • Multifractal based image processing for estimating the complexity of COVID-19 dynamics
    Q Rong, C Thangaraj, D Easwaramoorthy, S He
    The European Physical Journal Special Topics 230 (21), 3947-3954 , 2021
    2021
    Citations: 15

MOST CITED SCHOLAR PUBLICATIONS

  • Generation of fractals via iterated function system of Kannan contractions in controlled metric space
    C Thangaraj, D Easwaramoorthy, B Selmi, BP Chamola
    Mathematics and Computers in Simulation 222, 188-198 , 2024
    2024
    Citations: 34
  • Generalized fractal dimensions based comparison analysis of edge detection methods in CT images for estimating the infection of COVID-19 disease
    C Thangaraj, D Easwaramoorthy
    The European Physical Journal Special Topics 231 (18), 3717-3739 , 2022
    2022
    Citations: 18
  • Multifractal based image processing for estimating the complexity of COVID-19 dynamics
    Q Rong, C Thangaraj, D Easwaramoorthy, S He
    The European Physical Journal Special Topics 230 (21), 3947-3954 , 2021
    2021
    Citations: 15
  • Multifractal analysis in age-based classification for COVID-19 patients’ CT-scan images with different noise levels
    R Valarmathi, C Thangaraj, D Easwaramoorthy, B Selmi, H Jebali, ...
    Fluctuation and Noise Letters 23 (05), 2440055 , 2024
    2024
    Citations: 12
  • Multifractal analysis on age-based discrimination in X-ray images for sensing the severity of COVID-19 disease
    S He, C Thangaraj, D Easwaramoorthy, G Muhiuddin
    The European Physical Journal Special Topics 231 (18), 3663-3671 , 2022
    2022
    Citations: 9
  • Fractal based automatic detection of complexity in COVID‐19 X‐ray images
    C Thangaraj, D Easwaramoorthy, G Muhiuddin, B Selmi, V Kulish
    Expert Systems 42 (1), e13497 , 2025
    2025
    Citations: 8
  • Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems
    RA El-Nabulsi, C Thangaraj, R Valarmathi, W Anukool
    Chaos, Solitons & Fractals 200, 116974 , 2025
    2025
    Citations: 7
  • Fractals via controlled fisher iterated function system
    C Thangaraj, D Easwaramoorthy
    Fractal and Fractional 6 (12), 746 , 2022
    2022
    Citations: 5
  • Stability and chaos in nonstandard Hamiltonian planetary dynamics
    RA El-Nabulsi, W Anukool, C Thangaraj, R Valarmathi
    Chaos, Solitons & Fractals 202, 117410 , 2026
    2026
    Citations: 3
  • Extended Spin-Orbit Modeling of Unstable Discrete Fractional Hamiltonian Systems: Numerical Investigation of Chaotic Orbits for Mercury, Mars, Triton, and Sedna-like Trans …
    RA El-Nabulsi, W Anukool, R Valarmathi, C Thangaraj
    Advances in Space Research , 2026
    2026
    Citations: 1
  • Generation of Fractal Attractor for Controlled Metric Based Dynamical Systems
    C Thangaraj, R Valarmathi, D Easwaramoorthy, DR Kumar, B Prasad
    Contemporary Mathematics 5 (Issue 4), 6165 , 2024
    2024
    Citations: 1
  • Fractals via Self-Similar Group of Fisher Contractions
    C Thangaraj, D Easwaramoorthy
    International Conference on Recent Developments in Mathematics, 347-356 , 2022
    2022
    Citations: 1
  • Multifractal dimensions and fractional differentiation in automated edge detection on intuitionistic fuzzy enhanced image
    VP Ananthi, C Thangaraj, D Easwaramoorthy
    Frontiers of Fractal Analysis, 153-171 , 2022
    2022
    Citations: 1
  • Nonlocal Fractal Diffusion-Advection Models with Variable Coefficients and Nonlocal Time Delay: Existence of Solutions, Lyapunov Function, Hopf Bifurcation, and Stability
    RA El-Nabulsi, W Anukool, R Valarmathi, C Thangaraj
    Journal of Peridynamics and Nonlocal Modeling 8 (1), 6 , 2026
    2026
  • A unified fractional action integral framework for memory-dependent circuit dynamics and Josephson junctions
    RA El-Nabulsi, W Anukool, R Valarmathi, C Thangaraj
    Journal of Electronic Science and Technology, 100362 , 2026
    2026
  • Fractal Laplacian approach to quantum wave localization
    R Valarmathi, C Thangaraj, RA El-Nabulsi, W Anukool
    Modern Physics Letters A 41 (11), 2650047 , 2026
    2026
  • RGB image edge detection using fuzzy inference techniques
    TL Yookesh, M Loganathan, C Thangaraj, EB Kumar
    AIP Conference Proceedings 3348 (1), 020009 , 2026
    2026
  • Acceleration-dependent hamiltonian for the zeros of the riemann zeta function: Spectral properties and self-adjoint realizations of the new operator
    W Anukool, RA El-Nabulsi, R Valarmathi, C Thangaraj
    Modern Physics Letters A 41 (01), 2550219 , 2026
    2026
  • Fractals via Self-Similar Group of Fisher
    C Thangaraj, D Easwaramoorthy
    Recent Developments in Algebra and Analysis: International Conference on … , 2024
    2024