University of Kashan Mathematics Interdisciplinary Research 2538-3639 11 2 2026 06 01 A‎ ‎High-Performance‎ ‎Block-Based‎ ‎Computational Scheme for Solving Fractional Nonlinear Equations in Electrospinning Modeling 141 159 115535 10.22052/mir.2026.257657.1542 EN Hadis Azin ‎Department of Mathematics, ‎Faculty of Mathematical Sciences, Alzahra University, Tehran‎, ‎I‎. ‎R‎. ‎Iran Yadollah Ordokhan ‎Department of Mathematics, ‎Faculty of Mathematical Sciences, Alzahra University, Tehran‎, ‎I‎. ‎R‎. ‎Iran Journal Article 2025 09 25 ‎The Bratu-type equation of fractional order possesses considerable theoretical and applied importance‎, ‎as it generalizes a conventional nonlinear differential equation to model phenomena that exhibit inherent memory and non-local interactions‎, ‎which are crucial in fields such as nuclear reactor assessment and the electrospinning process of nanofibers‎. ‎This study presents an innovative block-by-block (multi-step) computational methodology that employs quadratic interpolation to attain high-order accuracy‎. ‎The approach ensures a convergence rate of order $\mathcal{O}(\tau^{4})$‎, ‎significantly enhancing numerical precision concerning the discretization parameter $\tau$‎. ‎Its practical utilization is illustrated through a dedicated algorithm tailored for the fractional Bratu problem‎. ‎The effectiveness and robustness of the proposed method are validated through numerical experiments‎, ‎showcasing its ability to deliver high-fidelity solutions‎. https://mir.kashanu.ac.ir/article_115535_82e493d701eec2022830cb861abcc1fd.pdf