Numerical Solution for Fractional-Order Mathematical Model of Immune-Chemotherapeutic Treatment for Breast Cancer Using Modified Fractional Formula

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-89
Published: Aug 16, 2023
Cite as:
Mamon Abu Hammad, Iqbal H. Jebril, Shameseddin Alshorm, Iqbal M. Batiha, Nancy Abu Hammad, Numerical Solution for Fractional-Order Mathematical Model of Immune-Chemotherapeutic Treatment for Breast Cancer Using Modified Fractional Formula, Int. J. Anal. Appl., 21 (2023), 89.

Main Article Content

Mamon Abu Hammad, Iqbal H. Jebril, Shameseddin Alshorm, Iqbal M. Batiha, Nancy Abu Hammad

Abstract

Cancer is a complex and diverse group of diseases characterized by the uncontrolled growth and spread of abnormal cells in the body. Tumors, which are commonly associated with cancer, refer to abnormal masses of tissue that can develop in various organs or tissues. Cancer can arise from almost any cell type in the body and can affect different organs and systems. The disease occurs when the normal processes of cell division and growth go awry, leading to the formation of malignant tumors. These tumors have the potential to invade nearby tissues and spread to distant parts of the body through a process known as metastasis. In this paper, we aim to present a numerical solution for a recent fractional-order model related to Immune-Chemotherapeutic Treatment for Breast Cancer (ICT) using a novel numerical scheme called the Modified Fractional Euler Method (MFEM). We will also compare our proposed scheme with the traditional numerical scheme, Fractional Euler Method (FEM), through numerical simulations.

Article Details

References

  1. M. Abaid Ur Rehman, J. Ahmad, A. Hassan, J. Awrejcewicz, W. Pawlowski, H. Karamti, F.M. Alharbi, The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease, Symmetry. 14 (2022), 1694. https://doi.org/10.3390/sym14081694.
  2. I.M. Batiha, A. Bataihah, Abeer A. Al-Nana, S. Alshorm, I.H. Jebril, A. Zraiqat, A Numerical Scheme for Dealing with Fractional Initial Value Problem, Int. J. Innov. Comput. Inform. Control. 19 (2023), 763-774. https://doi.org/10.24507/ijicic.19.03.763.
  3. Z. Sabir, M. Munawar, M.A. Abdelkawy, M.A.Z. Raja, C. Ünlü, M.B. Jeelani, A.S. Alnahdi, Numerical Investigations of the Fractional-Order Mathematical Model Underlying Immune-Chemotherapeutic Treatment for Breast Cancer Using the Neural Networks, Fractal Fract. 6 (2022), 184. https://doi.org/10.3390/fractalfract6040184.
  4. I.M. Batiha, S. Alshorm, I. Jebril, A. Zraiqat, Zaid Momani, S. Momani, Modified 5-Point Fractional Formula With Richardson Extrapolation, AIMS Math. 8 (2023), 9520-9534. https://doi.org/10.3934/math.2023480.
  5. F. Özköse, M.T. Şenel, R. Habbireeh, Fractional-Order Mathematical Modelling of Cancer Cells-Cancer Stem Cells-Immune System Interaction With Chemotherapy, Math. Model. Numer. Simul. Appl. 1 (2021), 67-83. https://doi.org/10.53391/mmnsa.2021.01.007.
  6. I.M. Batiha, S. Alshorm, A. Al-Husban, R. Saadeh, G. Gharib, S. Momani, The n-Point Composite Fractional Formula for Approximating Riemann-Liouville Integrator, Symmetry. 15 (2023), 938. https://doi.org/10.3390/sym15040938.
  7. E. Ucar, N. Ozdemir, E. Altun, Fractional Order Model of Immune Cells Influenced by Cancer Cells, Math. Model. Nat. Phenom. 14 (2019), 308. https://doi.org/10.1051/mmnp/2019002.
  8. M.M. Al-Shomrani, M.A. Abdelkawy, Numerical Simulation for Fractional-Order Differential System of a Glioblastoma Multiforme and Immune System, Adv. Differ. Equ. 2020 (2020), 516. https://doi.org/10.1186/s13662-020-02978-2.
  9. H. Yasmin, M. Abu Hammad, R. Shah, B.M. Alotaibi, Sherif.M.E. Ismaeel, S.A. El-Tantawy, On the Solutions of the Fractional-Order Sawada-Kotera-Ito Equation and Modeling Nonlinear Structures in Fluid Mediums, Symmetry. 15 (2023), 605. https://doi.org/10.3390/sym15030605.
  10. I.M. Batiha, L.B. Aoua, T.E. Oussaeif, A. Ouannas, S. Alshorman, I.H. Jebril, S. Momani, Common Fixed Point Theorem in Non-Archimedean Menger PM-Spaces Using CLR Property with Application to Functional Equations, IAENG Int. J. Appl. Math. 53 (2023), 1-9.
  11. M. Mhailan, M. Abu Hammad, M. Al Horani, R. Khalil, On Fractional Vector Analysis, J. Math. Comput. Sci. 10 (2020), 2320-2326. https://doi.org/10.28919/jmcs/4863.
  12. I.M. Batiha, Z. Chebana, T.E. Oussaeif, A. Ouannas, S. Alshorm, A. Zraiqat, Solvability and Dynamics of Superlinear Reaction Diffusion Problem with Integral Condition, IAENG Int. J. Appl. Math. 53 (2023), 1-9.
  13. A. Farah1, A. Dababneh, A. Zraiqat, On Non-Parametric Criteria for Random Communication and Processes Relationship, Int. J. Adv. Sci. Eng. 7 (2020), 1675-1690.
  14. I.M. Batiha, A. Obeidat, S. Alshorm, A. Alotaibi, H. Alsubaie, S. Momani, M. Albdareen, F. Zouidi, S.M. Eldin, H. Jahanshahi, A Numerical Confirmation of a Fractional-Order COVID-19 Model’s Efficiency, Symmetry. 14 (2022), 2583. https://doi.org/10.3390/sym14122583.
  15. A. Dababneh, A. Zraiqat, A. Farah, H. Al-Zoubi, M.A. Hammad, Numerical Methods for Finding Periodic Solutions of Ordinary Differential Equations With Strong Nonlinearity, J. Math. Comput. Sci. 11 (2021), 6910-6922. https://doi.org/10.28919/jmcs/6477.
  16. S. Noor, M.A. Hammad, R. Shah, A.W. Alrowaily, S.A. El-Tantawy, Numerical Investigation of Fractional-Order Fornberg–Whitham Equations in the Framework of Aboodh Transformation, Symmetry. 15 (2023), 1353. https://doi.org/10.3390/sym15071353.
  17. M.A. Hammad, I. Jebril, R. Khalil, Large Fractional Linear Type Differential Equations, Int. J. Anal. Appl. 21 (2023), 65. https://doi.org/10.28924/2291-8639-21-2023-65.
  18. A.H. Salas, M. Abu Hammad, B.M. Alotaibi, L.S. El-Sherif, S.A. El-Tantawy, Analytical and Numerical Approximations to Some Coupled Forced Damped Duffing Oscillators, Symmetry. 14 (2022), 2286. https://doi.org/10.3390/sym14112286.
  19. M.A. Hammad, Conformable Fractional Martingales and Some Convergence Theorems, Mathematics. 10 (2021), 6. https://doi.org/10.3390/math10010006.