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Dastmalchi Saei, farhad, Bidar yamchi, Azizeh, baghmishe, mehdi, allahviranloo, tofigh. (1401). Numerical solution of two-dimensional fractional integral differential equations with weak single kernels using Lagrange polynomials. , (), -. doi: 10.30495/jnrm.2022.66767.2300
farhad Dastmalchi Saei; Azizeh Bidar yamchi; mehdi baghmishe; tofigh allahviranloo. "Numerical solution of two-dimensional fractional integral differential equations with weak single kernels using Lagrange polynomials". , , , 1401, -. doi: 10.30495/jnrm.2022.66767.2300
Dastmalchi Saei, farhad, Bidar yamchi, Azizeh, baghmishe, mehdi, allahviranloo, tofigh. (1401). 'Numerical solution of two-dimensional fractional integral differential equations with weak single kernels using Lagrange polynomials', , (), pp. -. doi: 10.30495/jnrm.2022.66767.2300
Dastmalchi Saei, farhad, Bidar yamchi, Azizeh, baghmishe, mehdi, allahviranloo, tofigh. Numerical solution of two-dimensional fractional integral differential equations with weak single kernels using Lagrange polynomials. , 1401; (): -. doi: 10.30495/jnrm.2022.66767.2300

Numerical solution of two-dimensional fractional integral differential equations with weak single kernels using Lagrange polynomials

Journal of New Researches in Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 شهریور 1401  XML
نوع مقاله: research paper
شناسه دیجیتال (DOI): 10.30495/jnrm.2022.66767.2300
نویسندگان
farhad Dastmalchi Saei email orcid 1؛ Azizeh Bidar yamchi2؛ mehdi baghmishe3؛ tofigh allahviranloo4
1Academic staff member
2islamic azad university of tabriz
3tabriz university
4turkey university
چکیده
.The main goal of this article is to provide an approximate solution for two-dimensional fractional integral differential equations using orthogonal Lagrange polynomials, which is widely used in engineering problems. The obtained results show the efficiency and effectiveness of the method and also show the ability of the method to numerically solve some nonlinear models such as nonlinear partial differential equations that have special applications in engineering and nonlinear science problems. First, the shifted orthogonal Lagrange polynomials are defined and the properties of these polynomials are presented. Integration operation matrix and product operation matrix are introduced. Then, these properties are used together with two-dimensional nodes with weak single kernels using Lagrange polynomials to convert the given integral equation to solving nonlinear algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the new method. The obtained results show the efficiency and effectiveness of the method and also show the ability of the method to numerically solve some nonlinear models such as nonlinear partial differential equations that have special applications in engineering and nonlinear science problems.
کلیدواژه‌ها
Two-dimensional fractional differential integral equations؛ orthogonal Lagrange polynomials؛ operational matrix؛ weak singular kernels
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تعداد مشاهده مقاله: 97


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