Polynomial-Based Minimization Approach for Solving Fractional-Order Differential Equations of Bratu Type.

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Bibliographic Details
Title:	Polynomial-Based Minimization Approach for Solving Fractional-Order Differential Equations of Bratu Type.
Authors:	Oderinu, Razaq Adekola¹ raoderinu@lautech.edu.ng, Yahaya, Ahmed Adeyi² aayahaya@lautech.edu.ng, Taiwo, Musilimu³ musilimu.taiwo@fuhsi.edu.ng, Oyewumi, Adepeju Abimbola¹ aaoyewumi53@lautech.edu.ng, Salaudeen, Kafilat Adebimpe⁴ salaudeenka@eauedoyo.edu.ng
Source:	IAENG International Journal of Applied Mathematics. Jun2026, Vol. 56 Issue 6, p2196-2210. 15p.
Subjects:	Fractional differential equations, Polynomial approximation, Nonlinear boundary value problems, Collocation methods, Caputo fractional derivatives, Boundary value problems
Abstract:	This paper provides an effective polynomial-based minimization strategy using the collocation method to solve linear and non-linear fractional-order boundary value problems (BVPs). The Caputo fractional order derivative is employed, while the Lagrange interpolating polynomial and Newton divided difference polynomial are utilized as basis functions. The proposed method is capable of solving linear and nonlinear boundary value problems under various boundary conditions, including the Bratu-type equation with Robin and mixed boundary conditions. Numerical findings indicate the accuracy and efficiency of the suggested technique. In addition, the method revealed the non-local and hereditary properties peculiar to fractional-order differential equations, which many numerical methods cannot provide. The technique provided a valuable tool for solving complex fractional-order BVPs in different domains, including science, engineering, and technology. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This paper provides an effective polynomial-based minimization strategy using the collocation method to solve linear and non-linear fractional-order boundary value problems (BVPs). The Caputo fractional order derivative is employed, while the Lagrange interpolating polynomial and Newton divided difference polynomial are utilized as basis functions. The proposed method is capable of solving linear and nonlinear boundary value problems under various boundary conditions, including the Bratu-type equation with Robin and mixed boundary conditions. Numerical findings indicate the accuracy and efficiency of the suggested technique. In addition, the method revealed the non-local and hereditary properties peculiar to fractional-order differential equations, which many numerical methods cannot provide. The technique provided a valuable tool for solving complex fractional-order BVPs in different domains, including science, engineering, and technology. [ABSTRACT FROM AUTHOR]
ISSN:	19929978