Modeling and solving applied differential equations in Physics by Gamma interval functions
*Mehmet PakdemirliCorresponding authorpakdemirli@gmail.comDepartment of Mechanical Engineering45140 MuradiyeManisa Celal Bayar UniversityYunusemre, Manisa, Turkey0000-0003-1221-9387View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2025
- Published Online:
- 26 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2339
- Pages:
- 1–13
Abstract
Keywords
Subject Classifications
References
[1] C. H. Edward, D. E. Penney, and D. Calvis, Differential Equations and Boundary Value Problems, Pearson Education Inc., New York (2015).
[2] P. V. ONeil, Advanced Engineering Mathematics, Wodsworth Publishing Co., Belmont, California (1991).
[3] A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley and Sons, New York (1981).
[4] A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, John Wiley and Sons, New York (1979).
[5] A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics, John Wiley and Sons, New York (1995).
[6] F. S. Tse, I. E. Morse and R. T. Hinkle, Mechanical Vibrations, Theory and Applications, Allyn and Bacon Inc., Boston (1978).
[7] M. Pakdemirli, “The Drag Work Minimization Path for a Flying Object with Altitude-Dependent Drag Parameters,” Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, vol. 223, no. 5, pp. 1113-1116 (2009).
[8] Y. Aksoy and M. Pakdemirli, “New Perturbation-Iteration Solutions for Bratu-type Equations,” Computers & Mathematics with Applications, vol. 59, no. 8, pp. 2802-2808 (2010).
[9] Y. Aksoy, M. Pakdemirli, S. Abbasbandy and H. Boyacı, “New Perturbation-Iteration Solutions for Nonlinear Heat Transfer Equations,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22, no. 7, pp. 814-828 (2012).
[10] M. Pakdemirli, “Perturbation–iteration method for strongly nonlinear vibrations,” Journal of Vibration and Control, vol. 23, no. 6, pp. 959-969 (2017).
[11] E. Yaşar and Y. Yıldırım, “A procedure on the first integrals of second order nonlinear ordinary differential equations,” The European Physical Journal Plus, vol. 130, no. 12, pp. 240-244 (2015).
[12] M. Pakdemirli and V. Yıldız, “Nonlinear curve equations maintaining constant normal accelerations with drag induced tangential decelerations,” Zeitschrift fur Naturforschung A, vol. 78, no. 2, pp. 125-132 (2023).
[13] L. Ruby, “Applications of the Mathieu equation,” American Journal of Physics, vol. 64, no. 1, pp. 39-44 (1996).
[14] F. Al-Kindi, F. M. Mahomed and M. Ziad, “Integrability of systems of ordinary differential equations via Lie point symmetries,” Mathematical Methods in the Applied Sciences, vol. 44, no. 11, pp. 9373-9392 (2021).
[15] Z. Sabira, M. A. Z. Rajab, C. M. Khalique and C. Unlu, “Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation,” Mathematics and Computers in Simulation, vol. 185, pp. 799–812 (2021).
[16] I. T. Dolapci and M. Pakdemirli, “New perturbation-iteration solutions of singular Emden-Fowler equations,” Mathematics in Engineering, Science and Aerospace, vol. 13, no. 4, pp. 1015-1026 (2022).




