The semi-analytical solutions of single-variable conformable fractional differential equations
Abstract
This study is concerned with obtaining semi-analytical solutions of conformable fractional (CF) differential equations, which are formulated using the recently introduced concept of the CF derivative, with the aid of the CF differential transform method (CFDTM). The method considered is actually an adaptation of a method that has long been used in solving differential equations, applied to CF differential equations. This derivative-based method primarily aims to find the transformed form of each term in a differential equation in accordance with the method’s definitions and rules. The method has few applications to CF differential equations, and examples of its application to equations containing different types of terms are also rare. Therefore, this study aims to use equations containing less common terms in the literature. However, such equations are not easy to find in the literature. Therefore, we selected functions with high oscillations and generated equations using the inverse problem approach. This allows us to obtain more complex equations for testing the method. In this way, the conversion equivalents of the terms less encountered in the literature are shown.
Keywords
References
- Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57-66.
- Ajarmah, B. (2022). Fractional mass-spring-damper system described by conformable fractional differential transform method. In International Conference on Wave Mechanics and Vibrations, Cham: Springer International Publishing, 125-132.
- Chiranjeevi, T., Biswas, R. K. (2022). Application of conformable fractional differential transform method for fractional optimal control problems. IFAC-PapersOnLine, 55(1), 643-648.
- Günerhan, H., Yiğider, M., Manafian, J., Ilhan, O. A. (2021). Numerical solution of fractional order logistic equations via conformable fractional differential transform method. Journal of Interdisciplinary Mathematics, 24(5), 1207-1220.
- Khalil, R., Al Horani, M., Yousef, A., Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
- Özkan, O., Kurt, A. (2018). The analytical solutions for conformable integral equations and integro-differential equations by conformable Laplace transform. Optical and Quantum Electronics, 50(2), 81.
- Podlubny, I. (1999). Fractional differential equations, mathematics in science and engineering. Academic Press, San Diego, USA.
- Samko, S. G., Kilbas, A. A., Marichev, O. I. (1993) Fractional Integrals and Derivatives, Theory and Applications. Gordon and Breach Science Publishers, Switzerland.
Details
Primary Language
English
Subjects
Numerical Solution of Differential and Integral Equations, Numerical Analysis, Symbolic Calculation
Journal Section
Research Article
Publication Date
August 17, 2026
Submission Date
November 4, 2025
Acceptance Date
February 20, 2026
Published in Issue
Year 2026 Volume: 10 Number: 2
APA
Karaoğlu, O., & Soylu, Ö. (2026). The semi-analytical solutions of single-variable conformable fractional differential equations. Journal of Innovative Science and Engineering, 10(2), 264-270. https://doi.org/10.38088/jise.1796433
AMA
1.Karaoğlu O, Soylu Ö. The semi-analytical solutions of single-variable conformable fractional differential equations. JISE. 2026;10(2):264-270. doi:10.38088/jise.1796433
Chicago
Karaoğlu, Onur, and Özlem Soylu. 2026. “The Semi-Analytical Solutions of Single-Variable Conformable Fractional Differential Equations”. Journal of Innovative Science and Engineering 10 (2): 264-70. https://doi.org/10.38088/jise.1796433.
EndNote
Karaoğlu O, Soylu Ö (August 1, 2026) The semi-analytical solutions of single-variable conformable fractional differential equations. Journal of Innovative Science and Engineering 10 2 264–270.
IEEE
[1]O. Karaoğlu and Ö. Soylu, “The semi-analytical solutions of single-variable conformable fractional differential equations”, JISE, vol. 10, no. 2, pp. 264–270, Aug. 2026, doi: 10.38088/jise.1796433.
ISNAD
Karaoğlu, Onur - Soylu, Özlem. “The Semi-Analytical Solutions of Single-Variable Conformable Fractional Differential Equations”. Journal of Innovative Science and Engineering 10/2 (August 1, 2026): 264-270. https://doi.org/10.38088/jise.1796433.
JAMA
1.Karaoğlu O, Soylu Ö. The semi-analytical solutions of single-variable conformable fractional differential equations. JISE. 2026;10:264–270.
MLA
Karaoğlu, Onur, and Özlem Soylu. “The Semi-Analytical Solutions of Single-Variable Conformable Fractional Differential Equations”. Journal of Innovative Science and Engineering, vol. 10, no. 2, Aug. 2026, pp. 264-70, doi:10.38088/jise.1796433.
Vancouver
1.Onur Karaoğlu, Özlem Soylu. The semi-analytical solutions of single-variable conformable fractional differential equations. JISE. 2026 Aug. 1;10(2):264-70. doi:10.38088/jise.1796433
