Adomian Method for Solving Fractional Sturm-Liouville Problem with Eigenparameter-Dependent Boundary Conditions

Abdullah Kablan; Fulya Şahantürk

doi:https://doi.org/10.14445/22315373/IJMTT-V72I5P107

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 5 | Year 2026 | Article Id. IJMTT-V72I5P107 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I5P107

Adomian Method for Solving Fractional Sturm-Liouville Problem with Eigenparameter-Dependent Boundary Conditions

Abdullah Kablan, Fulya Şahantürk

Received	Revised	Accepted	Published
28 Mar 2026	30 Apr 2026	16 May 2026	29 May 2026

Citation :

Abdullah Kablan, Fulya Şahantürk, "Adomian Method for Solving Fractional Sturm-Liouville Problem with Eigenparameter-Dependent Boundary Conditions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 5, pp. 81-87, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I5P107

Abstract

This research focused on computing eigenvalues and eigenfunctions of a class of fractional Sturm-Liouville boundary value problems with eigenparameter-dependent boundary conditions using the Adomian Decomposition Method (ADM). Fractional differential equations provide an effective mathematical tool for modeling and simulating non-classical dynamic phenomena in physics, engineering, and applied sciences. The main novelty of this work lies in the use of the Adomian Decomposition Method for computing both eigenvalues and eigenfunctions of fractional Sturm-Liouville boundary value problems, where the forcing term is an arbitrary function of 𝑥 and 𝑦. The results indicate that the suggested method provides a simple and efficient alternative for the spectral analysis of fractional differential operators. At the end of the paper, the representative example is presented to demonstrate the applicability of the method.

Keywords

Adomian Decomposition Method, Eigenfunctions, Eigenvalues, Fractional differential equations, Sturm-Liouville problem.

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