1
Graduate Education Institute, University of Ondokuz Mayis, Samsun, Turkiye.
2
Department of Mathematics Education, University of Ondokuz Mayis, Samsun, Turkiye.
10.22034/cmde.2025.67942.3254
Abstract
In this study, concepts of variable-order β(μ)-derivative and β(μ)-integral are presented. It is proven properties such as differentiability, continuity, linearity, commutative, associative etc. of variable-order β(μ)-derivative. To prove that the generalized definition of the β(μ)-derivative is effective, applicable and useful, it is considered a differential equation of variable-order. It is demonstrated solvability of the Rosenau-Hynam equation with variable-order β(μ)-derivative as semi-analytical with the modified variational iteration method. It is examined the comparison of semi-analytical solutions with the exact solution and their oscillation. It is commented on the usefulness, effectiveness and reliability of modified variational iteration method for relevant equations. It is enriched semi-analytical solutions of the Rosenau-Hynam equation with variable β(μ)-orders such as trigonometric, exponential and hyperbolic functions. The results are interpreted with the help of tables and figures.
Aydin, E. and Cilingir Sungu, I. (2026). On the Variable-Order Beta Derivative with Properties and Applications. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.67942.3254
MLA
Aydin, E. , and Cilingir Sungu, I. . "On the Variable-Order Beta Derivative with Properties and Applications", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2025.67942.3254
HARVARD
Aydin, E., Cilingir Sungu, I. (2026). 'On the Variable-Order Beta Derivative with Properties and Applications', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.67942.3254
CHICAGO
E. Aydin and I. Cilingir Sungu, "On the Variable-Order Beta Derivative with Properties and Applications," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2025.67942.3254
VANCOUVER
Aydin, E., Cilingir Sungu, I. On the Variable-Order Beta Derivative with Properties and Applications. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2025.67942.3254
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