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A novel approach using a new generalization of Bernoulli wavelets for solving fractional integro-differential equations with singular kernel | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 دی 1403 اصل مقاله (2.14 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.62229.2728 | ||
| نویسنده | ||
| Somayeh Nemati* | ||
| Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. | ||
| چکیده | ||
| In recent years, various fractional-order basis functions have been constructed and used for solving different classes of fractional problems. In this work, a new generalization of fractional-order Bernoulli wavelets is introduced. These new basis functions are employed to give a numerical solution for Hammerstein type fractional integro-differential equations with weakly singular kernel. To this aim, the Riemann-Liouville integral operator is applied to the basis functions and the result is computed exactly by the analytic form of Bernoulli polynomials. Through this process, key properties of the Riemann-Liouville integral and Caputo derivative are utilized to define two remainders associated with the main problem. After that, using an appropriate set of collocation points, the problem is converted to a system of algebraic equations. Due to the efficiency and high accuracy of this new technique, we extend the method for solving fractional Fredholm-Volterra integro-differential equations. Then, an upper bound of the error is discussed for the approximation of a function based on the fractional-order Bernoulli wavelets. Finally, the method is utilized for solving some illustrative examples to check its performance. | ||
| کلیدواژه‌ها | ||
| Weakly singular fractional integro-differential equations؛ Generalized fractional-order Bernoulli wavelets؛ Caputo derivative؛ Riemann-Liouville integral | ||
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آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 72 |
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