Application of the Multistage Telescoping Decomposition Method for Solving Fractional Logistic Equations
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Authors:Muhammad Abdulkari1*, A. M. Kwami2, A. G. Madaki3, J. O. Okai4, J. M. Muhammad5
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Abstract
Classical logistic equations are widely used in population dynamics but cannot represent the memory and hereditary effects inherent in many real-world systems. This study applies the Multistage Telescoping Decomposition Method (MTDM) to fractional logistic differential equations formulated using the Caputo fractional derivative. The fractional logistic equation was reformulated, and MTDM was employed to obtain semi-analytical approximate solutions without requiring computationally intensive symbolic procedures such as Adomian polynomials or Lagrange multipliers. Numerical examples were used to evaluate the method’s accuracy, efficiency, and convergence across different fractional orders. The resulting solutions were compared with those obtained using the Telescoping Decomposition Method, New Iterative Method, and Residual Power Series Method. Error analyses and graphical comparisons demonstrate that MTDM produces highly accurate approximations, converges more rapidly, and reduces computational complexity relative to the comparison methods. These findings establish MTDM as an efficient semi-analytical approach for solving fractional logistic equations and demonstrate its broader potential for nonlinear fractional differential equations. The study contributes a practical computational framework for applications involving memory-dependent processes in applied mathematics, physics, and biological modeling.
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References
Adomian, G. (1994). Solving frontier problems of physics: The decomposition method. Kluwer Academic Publishers. https://doi.org/10.1007/978-94-015-8289-6
Atangana, A. (2014). On the fractional logistic equation. Advances in Difference Equations, 2014(1), Article 278.
Bhalekar, S., & Daftardar-Gejji, V. (2012). Solving fractional-order logistic equation using a new iterative method. International Journal of Differential Equations, 2012, Article 975829. https://doi.org/10.1155/2012/975829
Chita, F., Ayadi, S., Erden Ege, M., Ege, O., & Ramaswamy, R. (2025). A novel approach for solving fractional differential equations via a multistage telescoping decomposition method. Fractal and Fractional, 9(2), Article 65. https://doi.org/10.3390/fractalfract9020065
Daftardar-Gejji, V., & Jafari, H. (2006). An iterative method for solving nonlinear functional equations. Journal of Mathematical Analysis and Applications, 316(2), 753–763. https://doi.org/10.1016/j.jmaa.2005.05.009
Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Springer. https://doi.org/10.1007/978-3-642-14574-2
Dunnimit, P., Wiwatwanich, A., & Poltem, D. (2020). Solutions of the fractional logistics equations via the residual power series method with Adomian polynomials. International Journal of Mathematics and Computer Science, 15(3), 885–903.
Ege, O., Ayadi, S., & Erden Ege, M. (2023). Elzaki-based decomposition methods for fractional PDEs. Mathematics, 11(1), Article 105.
He, J.-H. (1999). Variational iteration method—a kind of non-linear analytical technique: Some examples. International Journal of Non-Linear Mechanics, 34(4), 699–708. https://doi.org/10.1016/S0020-7462(98)00048-1
He, J.-H. (2006). Homotopy perturbation method for solving boundary value problems. Physics Letters A, 350(1–2), 87–88. https://doi.org/10.1016/j.physleta.2005.10.005
Khan, S. U., Qureshi, M. Z., & Baleanu, D. (2022). Applications of Elzaki transform to fractional-order systems. Mathematics, 10(6), Article 1023.
Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Elsevier. https://doi.org/10.1016/S0304-0208(06)X8001-5
Liao, S. (2003). Beyond perturbation: Introduction to the homotopy analysis method. Chapman & Hall/CRC. https://doi.org/10.1201/9780203491164
Magin, R. L. (2006). Fractional calculus in bioengineering. Begell House.
Mainardi, F. (2010). Fractional calculus and waves in linear viscoelasticity: An introduction to mathematical models. Imperial College Press. https://doi.org/10.1142/p614
Manjak, N. H., Mishra, A. K., & Kabala, D. (2014). Telescoping decomposition method for solving second-order nonlinear differential equations. International Journal of Engineering Research & Technology, 3(2), 590–595.
Murray, J. D. (2002). Mathematical biology: I. An introduction (3rd ed.). Springer. https://doi.org/10.1007/b98868
Odibat, Z. M., & Shawagfeh, N. T. (2007). Generalized Taylor’s formula. Applied Mathematics and Computation, 186(1), 286–293. https://doi.org/10.1016/j.amc.2006.07.102
Podlubny, I. (1999). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press. https://doi.org/10.1016/S0076-5392(99)X8001-5
Sumiati, I., Johansyah, M. D., Rusyaman, E., & Supriatna, A. K. (2020). Numerical method for transient solution of the fractional logistic differential equation in population growth model. AIP Conference Proceedings, 2264(1), Article 040004. https://doi.org/10.1063/5.0023797
Tarasov, V. E. (2010). Fractional dynamics: Applications of fractional calculus to dynamics of particles, fields and media. Springer. https://doi.org/10.1007/978-3-642-14003-7
Verhulst, P. F. (1845). Recherches mathématiques sur la loi d’accroissement de la population. Nouveaux Mémoires de l’Académie Royale des Sciences et Belles-Lettres de Bruxelles, 18, 1–41.