Research Article
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Year 2023, Volume: 41 Issue: 2, 331 - 343, 30.04.2023

Hatıra Günerhan Mohammed Kaabar Ercan Celık

Abstract

References

  • REFERENCES
  • [1] Mahdy AMS, Mohamed MS, Gepreel KA, AL-Amiri A, Higazy M. Dynamical characteristics and signal flow graph of nonlinear fractional smoking mathematical model. Chaos Solitons Fractals 202;141:110308. [CrossRef]
  • [2] Ertürk VS, Zaman G, Momani S. A numeric–analytic method for approximating a giving up smoking model containing fractional derivatives. Comput Math Appl 2012;64:30653074. [CrossRef]
  • [3] Haq F, Shah K, ur Rahman G, Shahzad M. Numerical solution of fractional order smoking model via laplace Adomian decomposition method. Alexandria Eng J 2018;57:10611069. [CrossRef]
  • [4] Mahdy AMS, Sweilam NH, Higazy, M. Approximate solution for solving nonlinear fractional order smoking model, Alexandria Eng J 2020;59:739752. [CrossRef]
  • [5] Uçar S, Uçar E, Özdemir N, Hammouch Z. Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative Chaos Solitons Fractals 2019;118:300306. [CrossRef]
  • [6] Veeresha P, Prakasha DG, Baskonus HM. Solving smoking epidemic model of fractional order using a modified homotopy analysis transform method. Math Sci 2019;13:115128. [CrossRef]
  • [7] Ahmad A, Farman M, Ahmad MO, Raza N, Abdullah M. Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis. Int J Adv Appl Sci 2018;5:123129. [CrossRef]
  • [8] Sefidgar E, Celik E, Shiri B. Numerical solution of fractional differential equation in a model of HIV infection of CD4 (+) T cells. Int J Appl Math Statistics 2017;56:2332.
  • [9] Kaabar M. Novel methods for solving the conformable wave equation. J New Theory 2020;31:5685.
  • [10] Kaabar MKA, Martínez Gonzalez F, Gómez‐Aguilar JF, Ghanbari B, Kaplan M, Günerhan H. New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐ order spatio‐temporal dispersion via double Laplace transform method. Math Methods Appl Sci 2021;44:1113811156. [CrossRef]
  • [11] Martínez F, Martínez I, Kaabar MKA, Paredes S. New results on complex conformable integral. AIMS Math 2020;5:76957710. [CrossRef]
  • [12] Martínez F, Martínez I, Kaabar MKA, Ortiz-Munuera R, Paredes S. Note on the conformable fractional derivatives and integrals of complex-valued functions of a real variable. Int J Appl Math 2020;50:609615.
  • [13] Zhou JK. Differential Transformation and Its Applications for Electronic Circuits. China: Huazhong Science & Technology University Press; 2016.
  • [14] Arikoglu A, Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Solitons Fractals 2007;34:14731481. [CrossRef]
  • [15] Ali A, Ertürk VS, Zeb A, Khan RA. Numerical solution of fractional order immunology and aids model via laplace transform Adomian decomposition method. J Fract Calculus Appl 2019;10:242–252.
  • [16] Günerhan H, Dutta H, Dokuyucu MA, Adel W. Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators. Chaos Solitons Fractals 2020;139:110053. [CrossRef]
  • [17] Dokuyucu MA, Çelik E, Bulut H, Başkonuş HM. Cancer treatment model with the Caputo-Fabrizio fractional derivative. Eur Phys J Plus 2018;133:16. [CrossRef]
  • [18] Dokuyucu MA, Çelik E. Analyzing a novel coronavirus model (COVID-19) in the sense of caputo-fabrizio fractional operator. Appl Comput Math 2021;20:4969.
  • [19] Javed K, Uddin F, Aydi H, Arshad M, Ishtiaq U, Alsamir H. On fuzzy b-metric-like spaces. J Funct Spaces 2021:19. [CrossRef]
  • [20] Uddin F, Javed K, Aydi H, Ishtiaq U, Arshad M. Control fuzzy metric spaces via orthogonality with an application. J Math 2021:112. [CrossRef]
  • [21] Ishtiaq U, Javed K, Uddin F, Sen MDL, Ahmed K, Ali MU. Fixed point results in orthogonal neutrosophic metric spaces. Complexity 2021:118. [CrossRef]

Novel analytical and approximate-analytical methods for solving the nonlinear fractional smoking mathematical model

Year 2023, Volume: 41 Issue: 2, 331 - 343, 30.04.2023

Hatıra Günerhan Mohammed Kaabar Ercan Celık

Abstract

Smoking is globally a challenging issue that causes many fatal health problems. In this paper, a nonlinear fractional smoking mathematical model is proposed in the context of a modi-fied form of the Caputo fractional-order derivative. The analytical and approximate-analytical solutions are obtained for the proposed mathematical model via the fractional differential transform method (FDTM) and Laplace Adomian decomposition method (LADM). The ob-tained solution is provided as a rapidly convergent series. Simulation results are provided in this paper to compare the obtained solutions by FDTM, LADM, Runge Kutta (RK) method, and reduced differential transforms method (RDTM) with the exact solution of the proposed problem. By comparing both FDTM and LADM solutions, the FDTM solution is closer to the exact solution than the LADM solution. All obtained solutions have been analyzed and com-pared graphically to validate the effiency and applicability of all results.

Keywords

Mathematical Modelling Fractional Calculus Fractional Differential Transform Method (FDTM) Laplace Adomian Decomposition Method (LADM) Smoking Mathematical Model

References

  • REFERENCES
  • [1] Mahdy AMS, Mohamed MS, Gepreel KA, AL-Amiri A, Higazy M. Dynamical characteristics and signal flow graph of nonlinear fractional smoking mathematical model. Chaos Solitons Fractals 202;141:110308. [CrossRef]
  • [2] Ertürk VS, Zaman G, Momani S. A numeric–analytic method for approximating a giving up smoking model containing fractional derivatives. Comput Math Appl 2012;64:30653074. [CrossRef]
  • [3] Haq F, Shah K, ur Rahman G, Shahzad M. Numerical solution of fractional order smoking model via laplace Adomian decomposition method. Alexandria Eng J 2018;57:10611069. [CrossRef]
  • [4] Mahdy AMS, Sweilam NH, Higazy, M. Approximate solution for solving nonlinear fractional order smoking model, Alexandria Eng J 2020;59:739752. [CrossRef]
  • [5] Uçar S, Uçar E, Özdemir N, Hammouch Z. Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative Chaos Solitons Fractals 2019;118:300306. [CrossRef]
  • [6] Veeresha P, Prakasha DG, Baskonus HM. Solving smoking epidemic model of fractional order using a modified homotopy analysis transform method. Math Sci 2019;13:115128. [CrossRef]
  • [7] Ahmad A, Farman M, Ahmad MO, Raza N, Abdullah M. Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis. Int J Adv Appl Sci 2018;5:123129. [CrossRef]
  • [8] Sefidgar E, Celik E, Shiri B. Numerical solution of fractional differential equation in a model of HIV infection of CD4 (+) T cells. Int J Appl Math Statistics 2017;56:2332.
  • [9] Kaabar M. Novel methods for solving the conformable wave equation. J New Theory 2020;31:5685.
  • [10] Kaabar MKA, Martínez Gonzalez F, Gómez‐Aguilar JF, Ghanbari B, Kaplan M, Günerhan H. New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐ order spatio‐temporal dispersion via double Laplace transform method. Math Methods Appl Sci 2021;44:1113811156. [CrossRef]
  • [11] Martínez F, Martínez I, Kaabar MKA, Paredes S. New results on complex conformable integral. AIMS Math 2020;5:76957710. [CrossRef]
  • [12] Martínez F, Martínez I, Kaabar MKA, Ortiz-Munuera R, Paredes S. Note on the conformable fractional derivatives and integrals of complex-valued functions of a real variable. Int J Appl Math 2020;50:609615.
  • [13] Zhou JK. Differential Transformation and Its Applications for Electronic Circuits. China: Huazhong Science & Technology University Press; 2016.
  • [14] Arikoglu A, Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Solitons Fractals 2007;34:14731481. [CrossRef]
  • [15] Ali A, Ertürk VS, Zeb A, Khan RA. Numerical solution of fractional order immunology and aids model via laplace transform Adomian decomposition method. J Fract Calculus Appl 2019;10:242–252.
  • [16] Günerhan H, Dutta H, Dokuyucu MA, Adel W. Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators. Chaos Solitons Fractals 2020;139:110053. [CrossRef]
  • [17] Dokuyucu MA, Çelik E, Bulut H, Başkonuş HM. Cancer treatment model with the Caputo-Fabrizio fractional derivative. Eur Phys J Plus 2018;133:16. [CrossRef]
  • [18] Dokuyucu MA, Çelik E. Analyzing a novel coronavirus model (COVID-19) in the sense of caputo-fabrizio fractional operator. Appl Comput Math 2021;20:4969.
  • [19] Javed K, Uddin F, Aydi H, Arshad M, Ishtiaq U, Alsamir H. On fuzzy b-metric-like spaces. J Funct Spaces 2021:19. [CrossRef]
  • [20] Uddin F, Javed K, Aydi H, Ishtiaq U, Arshad M. Control fuzzy metric spaces via orthogonality with an application. J Math 2021:112. [CrossRef]
  • [21] Ishtiaq U, Javed K, Uddin F, Sen MDL, Ahmed K, Ali MU. Fixed point results in orthogonal neutrosophic metric spaces. Complexity 2021:118. [CrossRef]
There are 22 citations in total.

Details

Primary Language English
Subjects Structural Biology
Journal Section Research Articles
Authors

Hatıra Günerhan 0000-0002-7802-477X

Mohammed Kaabar 0000-0003-2260-0341

Ercan Celık 0000-0001-5971-7653

Publication Date April 30, 2023
Submission Date October 14, 2021
Published in Issue Year 2023 Volume: 41 Issue: 2

Cite

Vancouver Günerhan H, Kaabar M, Celık E. Novel analytical and approximate-analytical methods for solving the nonlinear fractional smoking mathematical model. SIGMA. 2023;41(2):331-43.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/