Teaching Mathematics
Undergraduate and postgraduate instruction, supported by a certified specialization in e-teaching and online training methods.
FRACTIONAL CALCULUS · FUNCTIONAL ANALYSIS · MATHEMATICAL MODELLING
Ph.D. Mathematics — Dr. Babasaheb Ambedkar Marathwada University, Chhatrapati Sambhajinagar, India
$${}^{H}D^{\alpha,\beta;\psi}_{a^{+}} x(t) = f\big(t, x(t), \mathcal{I}^{\alpha;\psi}_{a^{+}} x(t)\big)$$
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PUBLICATIONS
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CONFERENCE PRESENTATIONS
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DEGREES ACROSS
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COUNTRIES
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About
I work on fractional calculus: the branch of analysis that extends differentiation and integration to non-integer order.
Most of my research concerns generalized Hilfer type fractional integro-differential equations — questions of existence, uniqueness and stability for boundary value problems that classical integer-order calculus cannot describe. More recently I have applied conformable and fractional-order operators to biological systems, modelling HIV dynamics following stem cell transplantation and the spread of H1N1 infection.
I began in mathematics at Al-Aqsa University in Gaza, continued at the University of Madras in Chennai, and completed my doctorate at Dr. Babasaheb Ambedkar Marathwada University, where I am based today. Alongside fractional calculus, my broader interest is in functional analysis.
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Why Fractional Calculus
DEFINITION
An ordinary derivative is local. It describes a system by what is happening at a single instant, and nothing else.
A fractional derivative is not. A derivative of order $\alpha$ carries the whole history of the system with it. That makes it the natural language for processes with memory — viscoelastic materials, anomalous diffusion, groundwater moving through porous rock, an epidemic that remembers its own past.
My work asks what it means to solve such an equation, and under what conditions a solution exists at all.
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Research Structure
The theoretical framework connecting abstract functional analysis, fractional operator theory, and empirical physical and biological models.
Fractional Calculus (Core Theoretical Foundation)
↳ Linked with: Functional Analysis
↳ Bridges to: Hilfer-Type Integro-Differential Equations
↳ Foundation for: Boundary Value Problems & Conformable Derivatives
Hilfer type fractional integro-differential equations
↳ Operator extensions with generalized integral conditions
↳ Existence, uniqueness and Ulam-type stability proofs
Boundary Value Problems (BVPs)
↳ Nonlocal multi-point conditions & positive coefficients
↳ Directly feeds biological & groundwater flow simulations
Modified Conformable Derivatives
↳ Analytical Taylor series expansions
↳ Applied to HIV dynamics & H1N1 epidemic progression
Applied Mathematical Modelling
↳ HIV dynamics post stem cell transplantation
↳ Spread of H1N1 infection & groundwater flow in porous media
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Experience & Areas of Expertise
Fractional Calculus — Theory and Applications
The core of my doctoral work: operational definitions, existence and uniqueness results, and the numerical behaviour of fractional-order systems.
Hilfer-Type Integro-Differential Equations
Generalized Hilfer operators under boundary and nonlocal integral-multipoint conditions — the subject of four of my published papers.
Boundary Value Problems
Well-posedness and qualitative analysis for fractional BVPs, including cases with positive constant coefficients.
Conformable Fractional Derivatives
Modified conformable derivatives, their Taylor expansions, and their use as a tractable alternative to classical fractional operators.
Mathematical Modelling of Biological Systems
Fractional-order epidemic and infection models: HIV dynamics post stem cell transplantation, H1N1 infection, and flow through porous media.
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Academic Trajectory
2030 — Completed
Ph.D. Mathematics
Dr. Babasaheb Ambedkar Marathwada University, Chhatrapati Sambhajinagar, Maharashtra, India
2025–2025
M.Sc. Mathematics
University of Madras, Chennai, Tamil Nadu, India
2020–2020
B.A. Mathematics
Al-Aqsa University, Gaza, Palestine
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Fractional Dynamics
As $\alpha$ moves from 0 to 2, the curve passes continuously through the function, its first derivative, and its second derivative — occupying, at every value in between, a derivative of an order that classical calculus has no name for.
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Publications
2030
- Alkord, M. N., Shaikh, S. L., & Altalla, M. B. — On a Type of Differential Calculus in the Frame of Generalized Hilfer type fractional integro-differential equation. Nonlinear Functional Analysis and Applications, 83–98.
- Alkord, M. N., & Shaikh, S. L. — BVP for Generalized Hilfer Integrodifferential Equation with Positive Constant Coefficient. International Journal of Dynamics and Control, 12(1), 107–114.
- Altalla, M. B., Shanmukha, B., El-Ajou, A., & Alkord, M. N. — Taylor's Series in Terms of the Modified Conformable Fractional Derivative with Applications. Nonlinear Functional Analysis and Applications, 435–450.
- Eid, H. A. A., & Alkord, M. N. — Impact of Fractional Conformable Derivatives on a (H1N1) Infection Model. Nonlinear Functional Analysis and Applications, 597–620.
2030
- Alkord, M. N., Shaikh, S. L., Redhwan, S. S., & Abdo, M. S. — Qualitative Analysis for Fractional-Order Nonlocal Integral-Multipoint Systems via a Generalized Hilfer Operator. Nonlinear Functional Analysis and Applications, 537–555.
2030
- Alkord, M. N., Shaikh, S. L., & Redhwan, S. S. — The Generalized Hilfer-Type Integro-Differential Equation with Boundary Condition. Mathematics, Statistics and Engineering Applications, 71(4), 4639–4654.
- Latif, S. S., Malik, M. A., Zabeeh, M. M. M., & Alkord, M. — Mathematical Modelling of Ground Water Flow in Porous Media. In Ecoconscious Explorations — A Multidisciplinary Approach, 164.
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Conference Presentations
Nonlinear Fractional Modeling of HIV Infection with Stem Cell Transplantation: Stability and Numerical Observations
National Conference on Nonlinear Analysis and Applications (NCNAA-25) · 30–31 January 2025
Dr. Babasaheb Ambedkar Marathwada University, Chhatrapati Sambhajinagar, India
A Fractional Order Model of HIV Dynamics Post Stem Cell Transplantation: Insights from Conformable Fractional Derivatives and LC Operators
National Conference on Emerging Trends in Physics and Mathematics (ETPM-2024) · 5 September 2024
Anandrao Dhonde Alias Babaji Mahavidyalaya, in collaboration with IAPT RC 08F · Kada, Dist. Beed, Maharashtra, India
BVP for Generalized Hilfer type fractional integro-differential equation with Positive Constant Coefficient
International Conference on Fractional Calculus: Theory, Applications and Numerics (ICFCTAN) · 27–29 January 2023
National Institute of Technology Puducherry, Karaikal · Virtual
The Generalized Hilfer-Type Integro-Differential Equation with Boundary Condition
International Conference on Mathematics, Statistics and Applied Science (ICMASTAS-22) · 13 August 2022
Pune, India
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Professional Development
Research & publishing
- ChatGPT and Advanced AI Tools for Accelerating Research and Publications
- Multidisciplinary, Interdisciplinary Research & Innovation for Holistic Development
- AI Tools for Researchers: Research Writing Strategies and Ethical Considerations
- Differential Equations
- Research Paper Writing and Publishing Skills for SCOPUS and SCI Journals
- Springer Nature Author Workshop
Teaching
- E-Teaching and Training Specialist Certificate
Beyond mathematics
- Yoga and Wellness
- Human Rights Education for University Students
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Technical Skills & Languages
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Mathematical softwareMATLAB, Mathematica, LaTeX
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ProgrammingNumerical simulation of fractional-order systems
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Research toolsReference management, academic writing, data analysis
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DigitalAI-assisted research tools, e-learning platforms
| Arabic | Native |
| English | Fluent |
| Hindi | Conversational |
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References
Dr. Sadikali L. Shaikh
Professor & Head, Department of Mathematics
Maulana Azad College of Arts, Science and Commerce, Aurangabad, Maharashtra, India
Doctoral supervisor and co-author on four papers
Dr. Asma'a A. Al Derbashy
Associate Professor, Department of Education
Al-Aqsa University, Gaza, Palestine
Contact details available on request.
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The next problem
I'm open to research collaboration, teaching positions, and doctoral or post-doctoral opportunities in fractional calculus and applied analysis.