University of Tabriz Computational Methods for Differential Equations 2345-3982 13 4 2025 10 01 Spectral collocation algorithm for the fractional Bratu equation via Hexic shifted Chebyshev polynomials 1102 1116 18548 10.22034/cmde.2024.61045.2621 EN Ahmed Gamal Atta Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt. Jomana Farag Soliman Department of Mathematics, Faculty of Science, Galala University, Egypt. Elaf Wael Elsaeed Department of Mathematics, Faculty of Science, Galala University, Egypt. Mostafa Wael Elsaeed Department of Mathematics, Faculty of Science, Galala University, Egypt. Youssri Hassan Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt. Journal Article 2024 03 30 This paper offers a numerical collocation scheme for solving the fractional nonlinear Bratu differential equation. We obtain a system of nonlinear equations using our spectral collocation method, which we then solve iteratively using Newton’s method to obtain an approximate solution. Additionally, numerical comparisons are made between the proposed strategy and several numerical strategies documented in various literature. The numerical findings verify the accuracy, computational efficiency, and ease of use of the recommended approach https://cmde.tabrizu.ac.ir/article_18548_da542ee8bccee2b50a73b527aa8bc807.pdf