Research Article
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Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform

Year 2023, Issue: 43, 63 - 72, 30.06.2023

Haldun Alpaslan Peker Fatma Aybike Çuha

https://doi.org/10.53570/jnt.1267202

Abstract

Differential equations refer to the mathematical modeling of phenomena in various applied fields, such as engineering, physics, chemistry, astronomy, biology, psychology, finance, and economics. The solutions of these models can be more complicated than those of algebraic equations. Therefore, it is convenient to use integral transformations to attain the solutions of these models. In this study, we find exact solutions to two cardiovascular models through an integral transformation, namely the Kashuri Fundo transform. It can be observed that the considered transform is a practical, reliable, and easy-to-use method for obtaining solutions to differential equations.

Keywords

Kashuri Fundo transform inverse Kashuri Fundo transform cardiovascular models

References

  • Y. A. Çengel, W. J. Palm, Differential Equations for Engineers and Scientists, McGraw Hill, New York, 2012.
  • L. Debnath, D. Bhatta, Integral Transforms and Their Applications, 2nd Edition, Chapman and Hall/CRC, Boca Raton, 2007.
  • P. Städter, Y. Schälte, L. Schmiester, J. Hasenauer, P. L. Stapor, \emph{Benchmarking of Numerical Integration Methods for ODE Models of Biological Systems}, Scientific Reports 11 (2020) Article Number 2696 11 pages.
  • D. Hasdemir, H. C. J. Hoefsloot, A. K. Smilde, \emph{Validation and Selection of ODE Based Systems Biology Models: How to Arrive at More Reliable Decisions}, BMC Systems Biology 9 (2015) Article Number 32 19 pages.
  • A. Kashuri, A. Fundo, \emph{A New Integral Transform}, Advances in Theoretical and Applied Mathematics 8 (1) (2013) 27--43.
  • A. Kashuri, A. Fundo, M. Kreku, \emph{Mixture of A New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations}, Advances in Pure Mathematics 3 (3) (2013) 317--323.
  • A. Kashuri, A. Fundo, R. Liko, \emph{On Double New Integral Transform and Double Laplace Transform}, European Scientific Journal 9 (33) (2013) 1857--7881.
  • A. Kashuri, A. Fundo, R. Liko, \emph{New Integral Transform for Solving Some Fractional Differential Equations}, International Journal of Pure and Applied Mathematics 103 (4) (2015) 675--682.
  • A. Fundo, A. Kashuri, R. Liko, \emph{New Integral Transform in Caputo Type Fractional Difference Operator}, Universal Journal of Applied Science 4 (1) (2016) 7--10.
  • K. Shah, T. Singh, \emph{A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method}, Journal of Geoscience and Environment Protection 3 (4) (2015) 24--30.
  • K. Shah, T. Singh, \emph{The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology}, Open Journal of Applied Sciences 5 (11) (2015) 688--695.
  • K. Shah, T. Singh, B. Kılıçman, \emph{Combination of Integral and Projected Differential Transform Methods for Time-Fractional Gas Dynamics Equations}, Ain Shams Engineering Journal 9 (4) (2018) 1683--1688.
  • I. Sumiati, Sukono, A. T. Bon, \emph{Adomian Decomposition Method and the New Integral Transform}, in: C. Mbohwa (Ed.), Proceedings of the 2nd African International Conference on Industrial Engineering and Operations Management, Harare, 2020, pp. 7--10.
  • M. D. Johansyah, A. K. Supriatna, E. Rusyaman, J. Saputra, \emph{Solving the Economic Growth Acceleration Model with Memory Effects: An Application of Combined Theorem of Adomian Decomposition Methods and Kashuri–Fundo Transformation Methods}, Symmetry 14 (2) (2022) 192 18 pages.
  • H. A. Peker, F. A. Cuha, \emph{Application of Kashuri Fundo Transform and Homotopy Perturbation Methods to Fractional Heat Transfer and Porous Media Equations}, Thermal Science 26 (4A) (2022) 2877--2884.
  • F. A. Cuha, H. A. Peker, \emph{Solution of Abel's Integral Equation by Kashuri Fundo Transform}, Thermal Science 26 (4A) (2022) 3003--3010.
  • N. Helmi, M. Kiftiah, B. Prihandono, \emph{Penyelesaian Persamaan Diferensial Parsial Linear Dengan Menggunakan Metode Transformasi Artion-Fundo}, Buletin Ilmiah Matematika Statistika dan Terapannya 5 (3) (2016) 195--204.
  • K. B. Singh, \emph{Homotopy Perturbation New Integral Transform Method for Numeric Study of Space-and Time Fractional (N+1)-Dimensional Heat-and Wave-like Equations}, Waves Wavelets and Fractals 4 (1) (2018) 19--36.
  • N. Dhange, \emph{A New Integral Transform for Solution of Convolution Type Volterra Integral Equation of First Kind}, International Journal of Mathematics Trends and Technology 66 (10) (2020) 52--57.
  • N. Güngör, \emph{Solving Convolution Type Linear Volterra Integral Equations with Kashuri Fundo Transform}, Journal of Abstract and Computational Mathematics 6 (2) (2021) 1--7.
  • H. A. Peker, F. A. Cuha, B. Peker, \emph{Solving Steady Heat Transfer Problems via Kashuri Fundo Transform}, Thermal Science 26 (4A) (2022) 3011--3017.
  • H. A. Peker, F. A. Çuha, \emph{Application of Kashuri Fundo Transform to Decay Problem}, SDU Journal of Natural and Applied Sciences 26 (3) (2022) 546--551.
  • H. A. Peker, F. A. Çuha, B. Peker, \emph{Kashuri Fundo Transform for Solving Chemical Reaction Models}, in: T. Acar (Ed.), Proceedings of International E-Conference on Mathematical and Statistical Sciences: A Selçuk Meeting, Konya, 2022, pp. 145--150.
  • H. A. Peker, F. A. Çuha, \emph{Solving One-Dimensional Bratu's Problem via Kashuri Fundo Decomposition Method}, Romanian Journal of Physics 68 (5-6) (2023) (in press).
  • H. A. Peker, F. A. Çuha, B. Peker, \emph{Kashuri Fundo Decomposition Method for Solving Michaelis-Menten Nonlinear Biochemical Reaction Model}, MATCH Communications in Mathematical and in Computer Chemistry 90 (2) (2023) 315--332.
  • H. A. Peker, F. A. Çuha, \emph{Application of Kashuri Fundo Transform to Population Growth and Mixing Problem}, in: D. J. Hemanth, T. Yigit, U. Kose, U. Guvenc (Eds.), 4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering, Vol. 7 of \emph{Engineering Cyber-Physical Systems and Critical Infrastructures}, Springer, Cham, 2023, pp. 407--414.
  • Y. Pala, Modern Applied Differential Equations (in Turkish), Nobel Akademik Publishing, Ankara, 2013.
  • S. L. Ross, Differential Equations, 3rd Edition, John Wiley \& Sons, New York, 1984.

Year 2023, Issue: 43, 63 - 72, 30.06.2023

Haldun Alpaslan Peker Fatma Aybike Çuha

https://doi.org/10.53570/jnt.1267202

Abstract

References

  • Y. A. Çengel, W. J. Palm, Differential Equations for Engineers and Scientists, McGraw Hill, New York, 2012.
  • L. Debnath, D. Bhatta, Integral Transforms and Their Applications, 2nd Edition, Chapman and Hall/CRC, Boca Raton, 2007.
  • P. Städter, Y. Schälte, L. Schmiester, J. Hasenauer, P. L. Stapor, \emph{Benchmarking of Numerical Integration Methods for ODE Models of Biological Systems}, Scientific Reports 11 (2020) Article Number 2696 11 pages.
  • D. Hasdemir, H. C. J. Hoefsloot, A. K. Smilde, \emph{Validation and Selection of ODE Based Systems Biology Models: How to Arrive at More Reliable Decisions}, BMC Systems Biology 9 (2015) Article Number 32 19 pages.
  • A. Kashuri, A. Fundo, \emph{A New Integral Transform}, Advances in Theoretical and Applied Mathematics 8 (1) (2013) 27--43.
  • A. Kashuri, A. Fundo, M. Kreku, \emph{Mixture of A New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations}, Advances in Pure Mathematics 3 (3) (2013) 317--323.
  • A. Kashuri, A. Fundo, R. Liko, \emph{On Double New Integral Transform and Double Laplace Transform}, European Scientific Journal 9 (33) (2013) 1857--7881.
  • A. Kashuri, A. Fundo, R. Liko, \emph{New Integral Transform for Solving Some Fractional Differential Equations}, International Journal of Pure and Applied Mathematics 103 (4) (2015) 675--682.
  • A. Fundo, A. Kashuri, R. Liko, \emph{New Integral Transform in Caputo Type Fractional Difference Operator}, Universal Journal of Applied Science 4 (1) (2016) 7--10.
  • K. Shah, T. Singh, \emph{A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method}, Journal of Geoscience and Environment Protection 3 (4) (2015) 24--30.
  • K. Shah, T. Singh, \emph{The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology}, Open Journal of Applied Sciences 5 (11) (2015) 688--695.
  • K. Shah, T. Singh, B. Kılıçman, \emph{Combination of Integral and Projected Differential Transform Methods for Time-Fractional Gas Dynamics Equations}, Ain Shams Engineering Journal 9 (4) (2018) 1683--1688.
  • I. Sumiati, Sukono, A. T. Bon, \emph{Adomian Decomposition Method and the New Integral Transform}, in: C. Mbohwa (Ed.), Proceedings of the 2nd African International Conference on Industrial Engineering and Operations Management, Harare, 2020, pp. 7--10.
  • M. D. Johansyah, A. K. Supriatna, E. Rusyaman, J. Saputra, \emph{Solving the Economic Growth Acceleration Model with Memory Effects: An Application of Combined Theorem of Adomian Decomposition Methods and Kashuri–Fundo Transformation Methods}, Symmetry 14 (2) (2022) 192 18 pages.
  • H. A. Peker, F. A. Cuha, \emph{Application of Kashuri Fundo Transform and Homotopy Perturbation Methods to Fractional Heat Transfer and Porous Media Equations}, Thermal Science 26 (4A) (2022) 2877--2884.
  • F. A. Cuha, H. A. Peker, \emph{Solution of Abel's Integral Equation by Kashuri Fundo Transform}, Thermal Science 26 (4A) (2022) 3003--3010.
  • N. Helmi, M. Kiftiah, B. Prihandono, \emph{Penyelesaian Persamaan Diferensial Parsial Linear Dengan Menggunakan Metode Transformasi Artion-Fundo}, Buletin Ilmiah Matematika Statistika dan Terapannya 5 (3) (2016) 195--204.
  • K. B. Singh, \emph{Homotopy Perturbation New Integral Transform Method for Numeric Study of Space-and Time Fractional (N+1)-Dimensional Heat-and Wave-like Equations}, Waves Wavelets and Fractals 4 (1) (2018) 19--36.
  • N. Dhange, \emph{A New Integral Transform for Solution of Convolution Type Volterra Integral Equation of First Kind}, International Journal of Mathematics Trends and Technology 66 (10) (2020) 52--57.
  • N. Güngör, \emph{Solving Convolution Type Linear Volterra Integral Equations with Kashuri Fundo Transform}, Journal of Abstract and Computational Mathematics 6 (2) (2021) 1--7.
  • H. A. Peker, F. A. Cuha, B. Peker, \emph{Solving Steady Heat Transfer Problems via Kashuri Fundo Transform}, Thermal Science 26 (4A) (2022) 3011--3017.
  • H. A. Peker, F. A. Çuha, \emph{Application of Kashuri Fundo Transform to Decay Problem}, SDU Journal of Natural and Applied Sciences 26 (3) (2022) 546--551.
  • H. A. Peker, F. A. Çuha, B. Peker, \emph{Kashuri Fundo Transform for Solving Chemical Reaction Models}, in: T. Acar (Ed.), Proceedings of International E-Conference on Mathematical and Statistical Sciences: A Selçuk Meeting, Konya, 2022, pp. 145--150.
  • H. A. Peker, F. A. Çuha, \emph{Solving One-Dimensional Bratu's Problem via Kashuri Fundo Decomposition Method}, Romanian Journal of Physics 68 (5-6) (2023) (in press).
  • H. A. Peker, F. A. Çuha, B. Peker, \emph{Kashuri Fundo Decomposition Method for Solving Michaelis-Menten Nonlinear Biochemical Reaction Model}, MATCH Communications in Mathematical and in Computer Chemistry 90 (2) (2023) 315--332.
  • H. A. Peker, F. A. Çuha, \emph{Application of Kashuri Fundo Transform to Population Growth and Mixing Problem}, in: D. J. Hemanth, T. Yigit, U. Kose, U. Guvenc (Eds.), 4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering, Vol. 7 of \emph{Engineering Cyber-Physical Systems and Critical Infrastructures}, Springer, Cham, 2023, pp. 407--414.
  • Y. Pala, Modern Applied Differential Equations (in Turkish), Nobel Akademik Publishing, Ankara, 2013.
  • S. L. Ross, Differential Equations, 3rd Edition, John Wiley \& Sons, New York, 1984.
There are 28 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Article
Authors

Haldun Alpaslan Peker 0000-0002-1654-6425

Fatma Aybike Çuha 0000-0002-7227-2086

Publication Date June 30, 2023
Submission Date March 18, 2023
Published in Issue Year 2023 Issue: 43

Cite

APA Peker, H. A., & Çuha, F. A. (2023). Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform. Journal of New Theory(43), 63-72. https://doi.org/10.53570/jnt.1267202
AMA Peker HA, Çuha FA. Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform. JNT. June 2023;(43):63-72. doi:10.53570/jnt.1267202
Chicago Peker, Haldun Alpaslan, and Fatma Aybike Çuha. “Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform”. Journal of New Theory, no. 43 (June 2023): 63-72. https://doi.org/10.53570/jnt.1267202.
EndNote Peker HA, Çuha FA (June 1, 2023) Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform. Journal of New Theory 43 63–72.
IEEE H. A. Peker and F. A. Çuha, “Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform”, JNT, no. 43, pp. 63–72, June 2023, doi: 10.53570/jnt.1267202.
ISNAD Peker, Haldun Alpaslan - Çuha, Fatma Aybike. “Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform”. Journal of New Theory 43 (June 2023), 63-72. https://doi.org/10.53570/jnt.1267202.
JAMA Peker HA, Çuha FA. Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform. JNT. 2023;:63–72.
MLA Peker, Haldun Alpaslan and Fatma Aybike Çuha. “Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform”. Journal of New Theory, no. 43, 2023, pp. 63-72, doi:10.53570/jnt.1267202.
Vancouver Peker HA, Çuha FA. Exact Solutions of Some Basic Cardiovascular Models by Kashuri Fundo Transform. JNT. 2023(43):63-72.
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