Abeer Al-nana
Department of Mathematics, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia.

Iqbal M. Batiha
Department of Mathematics, Al Zaytoonah University of Jordan, 11733, Amman, Jordan. & Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates.

Iqbal H. Jebril
Department of Mathematics, Al Zaytoonah University of Jordan, 11733, Amman, Jordan.

Shawkat Alkhazaleh
Department of Mathematics, Faculty of Sciences and Information Technology, Jadara University, Irbid, Jordan.

Thabet Abdeljawad
Department of Mathematics, Prince Sultan University, Riyadh, Saudi Arabia. & Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, 0208, Ga-Rankuwa, South Africa. & Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, 32093, Hawally, Kuwait.

DOI https://doi.org/10.33889/IJMEMS.2025.10.1.011

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Abstract

This paper presents the so-called shifted Jacobi method, an efficient numerical technique to solve second-order periodic boundary value problems with finitely many singularities involving nonlinear systems of two points. The method relies on the Jacobi polynomials used as natural basis functions in the conformable sense of fractional derivative. A study is carried out to compare the outcomes of the shifted Jacobi approach with those of other methods that are currently in use. In the same vein, a theoretical result for establishing a bound of the error generated from the proposed approximate solution is proved accordingly. The efficiency and effectiveness of the shifted Jacobi technique with conformable fractional derivative are discussed numerically.

Keywords- Conformable fractional derivative, Nonlinear boundary value problems, Nonlinear fractional differential equations, Jacobi orthogonal polynomials.

Citation

Al-nana, A., Batiha, I. M. Jebril, I. H. Alkhazaleh, S., & Abdeljawad, T. (2025). Numerical Solution of Conformable Fractional Periodic Boundary Value Problems by Shifted Jacobi Method. International Journal of Mathematical, Engineering and Management Sciences, 10(1), 189-206. https://doi.org/10.33889/IJMEMS.2025.10.1.011.