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On the Variable-Order Beta Derivative with Properties and Applications | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 فروردین 1405 اصل مقاله (1.24 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.67942.3254 | ||
| نویسندگان | ||
| Emre Aydin* 1؛ Inci Cilingir Sungu2 | ||
| 1Graduate Education Institute, University of Ondokuz Mayis, Samsun, Turkiye. | ||
| 2Department of Mathematics Education, University of Ondokuz Mayis, Samsun, Turkiye. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Variable-order β(μ)-derivative؛ Variable-order β(μ)-integral؛ Generalized variable-order β(μ)-derivative؛ Modified variational iteration method؛ The Rosenau-Hynam equation | ||
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آمار تعداد مشاهده مقاله: 9 تعداد دریافت فایل اصل مقاله: 21 |
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