A spectral collocation framework for fractional ODEs with nonlocal boundary conditions

Saleh Hadi, Mohammad; Lakestani, Mehrdad; Nemati Saray, Behzad

doi:10.22124/jmm.2026.33316.3040

A spectral collocation framework for fractional ODEs with nonlocal boundary conditions

Articles in Press

Document Type : Research Article

Authors

¹ Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran

² Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran and Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, T\"{u}rkiye

³ Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

10.22124/jmm.2026.33316.3040

Abstract

Fractional differential equations (FDEs) with nonlocal boundary conditions naturally arise in models of heat conduction, viscoelasticity, anomalous diffusion, and population dynamics, where both memory effects and global constraints must be considered. Their numerical treatment is challenging due to the interplay between fractional operators and nonlocal conditions. In this work, we propose a collocation method based on orthogonal cardinal functions for solving fractional ordinary differential equations with nonlocal boundary conditions. To enable an accurate numerical approximation, the desired problem is first transformed into an equivalent Volterra integral equation. The orthogonal property of the cardinal functions guarantees stability and spectral accuracy, and their interpolation property makes it easier to enforce nonlocal constraints. Through numerical experiments, we verify the scheme's accuracy and efficiency and investigate a priori error estimates. In comparison to existing numerical methods, the creative application of orthogonal cardinal functions within a collocation framework offers an effective and reliable tool for fractional models with increased accuracy.

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