Research Article

Year 2024,
Volume: 21 Issue: 1, 1 - 5, 01.05.2024
### Abstract

### References

- W. N. Mathews Jr., M. A. Esrick, Z.Y. Teoh, and J. K. Freericks, “A physicist’s guide to the solution of Kummar’s equation and confluent Hypergeometric functions,” Condensed Matter Physics, vol. 25, no. 3, pp. 1-23, 2021.
- F. W. J. Olver (Ed.), NIST handbook of mathematical functions hardback and CD-ROM. Cambridge University Press, 2010.
- W. Mgnus, F. Oberhettinger, R.P. Soni, Formulas and theorems for the special functions of mathematical physics. Springer-Verlag, Berlin, 1966.
- M. P. Chaudhary, M. L. Kaurangini, I. O. Kiymaz, U. M. Abubakar, and E. Ata, “Fractional integrations for the new generalized hypergeometric functions,” Journal of Ramanujan Society of Mathematical Science, vol. 10, no. 2, pp. 77-100, 2023.
- F. Ghanim, H. F. Al-Janaby, and M. Al-Momani, “A new Euler-beta function model with statistical implementation related to the Mittag-Leffler-Kumar function,” Kuwait Journal of Science, vol. 2023, pp. 1-27, 2023.
- S. Q. Hasan, U. M. Abubakar, and M. L. Kaurangini, “The new integral transform ‘’SUM transform’’ and its properties,” Palestine Journal of Mathematics, vol. 12 (Special Issue I), pp. 30-45, 2023.
- S. Q. Hasan, A. I. Mansour, and U. M. Abubakar, “Applications of the Sum integral transform in science and technology,” Wasit Journal for Pure Science, vol. 2, no. 3, pp. 29-40, 2023.
- R. P. Sharma, S. R. Mishra, and G. K. Panda, “Radiation absorption impact on the thermophysical properties of Cu and TiO2-water nanofluids: Laplace transform technique,’’ International Journal of Modern Physics B, pp. 2450238, 2023.
- C. Fetecau, I. A. Mirza, and D. Vieru, “Hydrodynamic permeability in axisymmetric flows of viscous fluids through an annular domain with porous layer,” Symmetry, vol. 15, no. 585, 2023.
- F. Ali, A. Zaib, and M. Khalid, “Unsteady MHD flow of Casson fluid past verticle surface using Laplace transform solution,” Journal of Computational Biophysics and Chemistry, vol. 22, no. 3, pp. 361-370, 2023.
- B.T. Sundari and R. Vijayalakshmi, “Exact solution for HMT effects on MHD Jeffrey fluid flow in the presence of porous medium by Laplace transform technique,” JP Journal of Heat and Mass Transfer, vol. 34, pp. 19-34, 2023.
- M. Sadaf, Z. Perveen, I. Zainab, G. Akram, M. Abbas, and D. Baleanu, “Dynamics of unsteady fluid-flow caused by a sinusoidally varying pressure gradient through a capillary tube with Caputo-Fabrizio derivative,” Thermal Science, vol. 27 (Spec. Issue 1), pp. 49-56, 2023.
- N. L. Shah, S. Rehman, D. Vieru, and S-J. Yook, “Unsteady flows of micropolar fluid parallel to the axis of an annular domain with a porous layer,” Alexandria Engineering Journal, vol. 76, no. 1, pp. 275-286, 2023.
- P. P. Dyke, An introduction to Laplace transforms and Fourier series, Springer, London, 2014.
- L. C. Andrews, Special functions of mathematics for engineers, Oxford Science Publication, Oxford, 1992.

The objective of this paper is to obtain solution to unsteady fluid flow through porous horizontal channel with injection and suction velocities using SUM integral transform. The solution is represented in terms of extended special function that contained two Fox-Wright functions in its kernel.

SUM transform Laplace transform Extended Hypergeometric Function Fluid flow Injection and Sunction Velocity

- W. N. Mathews Jr., M. A. Esrick, Z.Y. Teoh, and J. K. Freericks, “A physicist’s guide to the solution of Kummar’s equation and confluent Hypergeometric functions,” Condensed Matter Physics, vol. 25, no. 3, pp. 1-23, 2021.
- F. W. J. Olver (Ed.), NIST handbook of mathematical functions hardback and CD-ROM. Cambridge University Press, 2010.
- W. Mgnus, F. Oberhettinger, R.P. Soni, Formulas and theorems for the special functions of mathematical physics. Springer-Verlag, Berlin, 1966.
- M. P. Chaudhary, M. L. Kaurangini, I. O. Kiymaz, U. M. Abubakar, and E. Ata, “Fractional integrations for the new generalized hypergeometric functions,” Journal of Ramanujan Society of Mathematical Science, vol. 10, no. 2, pp. 77-100, 2023.
- F. Ghanim, H. F. Al-Janaby, and M. Al-Momani, “A new Euler-beta function model with statistical implementation related to the Mittag-Leffler-Kumar function,” Kuwait Journal of Science, vol. 2023, pp. 1-27, 2023.
- S. Q. Hasan, U. M. Abubakar, and M. L. Kaurangini, “The new integral transform ‘’SUM transform’’ and its properties,” Palestine Journal of Mathematics, vol. 12 (Special Issue I), pp. 30-45, 2023.
- S. Q. Hasan, A. I. Mansour, and U. M. Abubakar, “Applications of the Sum integral transform in science and technology,” Wasit Journal for Pure Science, vol. 2, no. 3, pp. 29-40, 2023.
- R. P. Sharma, S. R. Mishra, and G. K. Panda, “Radiation absorption impact on the thermophysical properties of Cu and TiO2-water nanofluids: Laplace transform technique,’’ International Journal of Modern Physics B, pp. 2450238, 2023.
- C. Fetecau, I. A. Mirza, and D. Vieru, “Hydrodynamic permeability in axisymmetric flows of viscous fluids through an annular domain with porous layer,” Symmetry, vol. 15, no. 585, 2023.
- F. Ali, A. Zaib, and M. Khalid, “Unsteady MHD flow of Casson fluid past verticle surface using Laplace transform solution,” Journal of Computational Biophysics and Chemistry, vol. 22, no. 3, pp. 361-370, 2023.
- B.T. Sundari and R. Vijayalakshmi, “Exact solution for HMT effects on MHD Jeffrey fluid flow in the presence of porous medium by Laplace transform technique,” JP Journal of Heat and Mass Transfer, vol. 34, pp. 19-34, 2023.
- M. Sadaf, Z. Perveen, I. Zainab, G. Akram, M. Abbas, and D. Baleanu, “Dynamics of unsteady fluid-flow caused by a sinusoidally varying pressure gradient through a capillary tube with Caputo-Fabrizio derivative,” Thermal Science, vol. 27 (Spec. Issue 1), pp. 49-56, 2023.
- N. L. Shah, S. Rehman, D. Vieru, and S-J. Yook, “Unsteady flows of micropolar fluid parallel to the axis of an annular domain with a porous layer,” Alexandria Engineering Journal, vol. 76, no. 1, pp. 275-286, 2023.
- P. P. Dyke, An introduction to Laplace transforms and Fourier series, Springer, London, 2014.
- L. C. Andrews, Special functions of mathematics for engineers, Oxford Science Publication, Oxford, 1992.

There are 15 citations in total.

Primary Language | English |
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Subjects | Partial Differential Equations, Mathematical Methods and Special Functions, Theoretical and Applied Mechanics in Mathematics |

Journal Section | Articles |

Authors | |

Publication Date | May 1, 2024 |

Submission Date | November 29, 2023 |

Acceptance Date | March 25, 2024 |

Published in Issue | Year 2024 Volume: 21 Issue: 1 |