18 خرداد 1402 # سمیه نعمتی

مرتبه علمی: دانشیار
نشانی:
تحصیلات: دکترای تخصصی / ریاضی کاربردی
تلفن: 01135302419
دانشکده: دانشکده علوم ریاضی

## مشخصات پژوهش

 عنوان Legendre wavelet collocation method combined with the Gauss-Jacobi quadrature for solving fractional delay-type integro-differential equations نوع پژوهش مقاله چاپ شده کلیدواژه‌ها Fractional delay-type integro-differential equations Legendre wavelet Gauss–Jacobi quadrature Chebyshev collocation points مجله APPLIED NUMERICAL MATHEMATICS شناسه DOI 10.1016/j.apnum.2019.05.024 پژوهشگران a { color: #4f98b0; } a:hover { color: #ffab00; } a:link:visited { text-decoration: none; } سمیه نعمتی (نفر اول) ، پدرو لیما (نفر دوم) ، سلمه صداقت (نفر سوم)

## چکیده

In this work, we present a collocation method based on the Legendre wavelet combined with the Gauss–Jacobi quadrature formula for solving a class of fractional delay-type integro-differential equations. The problem is considered with either initial or boundary conditions and the fractional derivative is described in the Caputo sense. First, an approximation of the unknown solution is considered in terms of the Legendre wavelet basis functions. Then, we substitute this approximation and its derivatives into the considered equation. The Caputo derivative of the unknown function is approximated using the Gauss–Jacobi quadrature formula. By collocating the obtained residual at the well-known shifted Chebyshev points, we get a system of nonlinear algebraic equations. In order to obtain a continuous solution, some conditions are added to the resulting system. Some error bounds are given for the Legendre wavelet approximation of an arbitrary function. Finally, some examples are included to show the efficiency and accuracy of this new technique.