iosr-Jm   Volume-22 ~ Issue-3 ~ May – June 2026

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Abstract : In this article we present a dynamical analysis of public debt that integrates regulatory interference and political pressure. We have modified the classical debt-growth model by including saturation effects, regulatory inertia, and bounded political pressures. Using Runge-Kutta 4th order integration, we have investigated the stability and bifurcation characteristics of the proposed financial dynamics system to understand how key parameters influence the system's....

Keywords: Stability; Bifurcation; Debt-Growth, Political intervention

[1] Goodwin, R. M. (1967). A Growth Cycle. In Socialism, Capitalism and Economic Growth. Cambridge: Cambridge University Press.
[2] Kaldor, N. (1940). A model of the trade cycle. The Economic Journal, 50, 78–92.
[3] Huang, D. S., & Li, H. Q. (1993). Theory and Method of Nonlinear Economics. Chengdu: Sichuan University Press.
[4] Ma, J., & Chen, Y. (2001). Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system. Applied Mathematics and Mechanics, 22, 1375–1382.
[5] Gao, Q., & Ma, J. (2009). Chaos and Hopf bifurcation of a finance system. Nonlinear Dynamics, 58, 209–216. https://doi.org/10.1007/s11071-009-9472-5.

Abstract : Mathematical models play a significant role in capturing dynamics of the biological models which explains the non-linear phenomena in living organisms. In this article, we study mathematical model of human liver via a numerical approach called Genocchi wavelet collocation method. The primary objective of this study is explore and determine the results for system of ordinary differential equations arising in the considered mathematical model and to investigate the dynamical aspects model. This model consists of two system of equations that is Bromsulphthalein (BDP) content....

Keywords: Liver model; Collocation method; Mathematical Modeling; Numerical Simulation.

[1] Abdel-Misih, S. R., Bloomston, M. (2010). Liver anatomy. Surgical Clinics, 90(4), 643-653.
[2] Celechovsk, L. (2004). A simple mathematical model of the human liver. Applications of Mathematics, 49(3), 227-246.
[3] Baleanu, D., Jajarmi, A., Mohammadi, H., Rezapour, S. A new study on the mathematical modelling of human liver with Caputo-
Fabrizio fractional derivative. Chaos, Solitons Fractals, 134, 109705, 2020.
[4] Calvetti D, Kuceyeski A and Somersalo E 2007 Sampling-based analysis of a spatially distributed model for liver metabolism at steady
state Multi. Model. and Simul.
[5] Chalhoub, E., Xie, L., Balasubramanian, V., Kim, J., Belovich, J. (2007). A distributed model of carbohydrate transport and metabolism
in the liver during rest and high-intensity exercise. Annals of Biomedical Engineering, 35(3), 474-491.

Abstract : This paper develops a shifted Chebyshev Operational matrix method for the numerical solution of fractional Abel integral equations involving weakly singular kernel. The proposed technique of the paper is based on the fractional order operational matrices of integration and differentiation of shifted Chebyshev polynomials. A theoretical error analysis of the proposed method is presented. Convergence results are established and an upper bound for an approximate error is derived, demonstrating that the accuracy improves as the degree of approximation increases....

Keywords: Fractional Abel integral equations, Fractional order operational matrix, Shifted Chebyshev polynomials.

[1] F. Mainardi, Fractional Calculus, Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien, 1997.
[2] R. L. Magrin, Fractional Calculus in bioengineering, part 1, Crit. Rev.𝑇𝑀Biomed. Eng. 32 (1) (2004).
[3] R. L. Bagley, P. J. Torvik, Fractional calculus-a different approach to the analysis of viscoelasticity damped structures, AIAA J. 21(5) (1983) 741-748.
[4] R. L. Bagley, P. J. Torvik, Fractional calculus in the transient analysis of Visco elastically damped structures, AIAA J. 23(6) (1985) 918-925.
[5] A. Gupta, R. K. Pandey, Adaptive Huber Scheme for Weakly Singular Fractional Integro-differential Equations, Diff. Equ. and Dyn. Sys. 28 (7) (2020).

Abstract : The Rosenbrock function is one of the most widely used benchmark problems for evaluating the robustness and convergence behavior of nonlinear optimization algorithms due to its narrow curved valley and ill-conditioned landscape. Classical optimization methods often exhibit difficulties in balancing convergence speed, nu-merical stability, and step acceptance when navigating such challenging regions. In this study, a Dual-Regulated Levenberg–Marquardt Trust Region Method (DR-LM-TRM) is proposed for unconstrained nonlinear optimization. The proposed frame-work combines the curvature regularization....

Keywords: Rosenbrock Function, Trust Region Method, Levenberg–Marquardt Method, Nonlinear Optimization, Second-Order Methods, Convergence Analysis, Adaptive Damping.

[1] Dennis, J. E. and Schnabel, R. B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ.
[2] Fletcher, R. (1987). Practical Methods of Optimization, 2nd Edition. John Wiley & Sons, Chichester, UK.
[3] Nocedal, J. and Wright, S. J. (2006). Numerical Optimization, 2nd Edition. Springer, New York.
[4] Conn, A. R., Gould, N. I. M. and Toint, P. L. (2000). Trust Region Methods. SIAM, Philadelphia.
[5] Rosenbrock, H. H. (1960). An Automatic Method for Finding the Greatest or Least Value of a Function. The Computer Journal, 3(3), 175–184..

Abstract : In this paper a new Weighted SNA integral transform is introduced which is defined as.

Keywords: Weighted Laplace type transform, Integral transform, Laplace transform, Convolution.

[1] Atangana, A; Kilicman, A. A novel integral operator transform and its application to some FODE and FPDE with some kind of singularities, Math.Prob.Eng.2013[cross Ref]
[2] Debnath, L., & Bhatta, D. (2014). Integral Transforms and Their Applications (3rd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b17670
[3] Elzaki T. M, “The new integral transform” Elzaki Transform” Glob J. Pure Appl Math 2011,7,57-64
[4] Hirschman, I. I. 1922-. (1955). The convolution transform. Princeton: Princeton University Press.
[5] Hirschman, Jr., I. I. An Introduction to Transform Theory (D. V. Widder), SIAM Review, 15(2) (396-397), 1973

Abstract : With a focus on core learning, multimodal education, experiential pedagogy, ongoing professional development, and teacher empowerment, the National Education Policy 2020 (NEP 2020) represents a thorough overhaul of India's educational system. Under NEP-2020, mathematics, which has traditionally been taught as an abstract, procedural subject, is especially positioned to become more conceptual, application-oriented, and integrated with other fields. In order to provide an organised, evidence-based explanation of how the role of the mathematics teacher......

Keywords: NEP-2020, mathematics education, teacher role, pedagogy, CPD, NPST, etc.

[1]. Ministry of Education (Government of India). National Education Policy 2020 (Full text). New Delhi: Government of India. Available: NEP 2020 PDF.
[2]. Ministry of Education. NEP Implementation — SARTHAQ and achievements report.
[3]. NCERT. Guidelines for 50 Hours of Continuous Professional Development for Teachers (2022).
[4]. NCTE. National Professional Standards for Teachers (NPST) – Guiding Document.
[5]. Selected literature on NEP and teachers (commentaries and research articles). Examples: IJR R Journal: “Exploring the Role of Teachers as Reflected in NEP 2020”.