Positive Solutions for a Conformable Fractional Boundary Value Problem with a Numerical Approach

Ahmadkhanlu, Asghar; Mohebbi, Roya; Erturk, Vedat Suat; Khani, Ali

doi:10.22034/cmde.2025.65862.3053

Positive Solutions for a Conformable Fractional Boundary Value Problem with a Numerical Approach

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

² Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayıs University, Samsun, Türkiye .

10.22034/cmde.2025.65862.3053

Abstract

This work introduces a novel approach to analyzing a class of conformable fractional boundary value problems. By employing a combination of standard and newly developed fixed-point theorems, we establish sufficient conditions for the existence and uniqueness of positive solutions. The proposed method offers several advantages over traditional techniques, including its simplicity and computational efficiency. Moreover, we construct a sequence of successive approximations that converge to the unique positive solution, providing a practical tool for numerical simulations. Our findings have significant implications for various fields, including physics, engineering, and biology, where conformable fractional differential equations are used to model complex phenomena.

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