Numerical Investigation of Fredholm Fractional Integro-differential Equations by Least Squares Method and Compact Combination of Shifted Chebyshev Polynomials

被引：2

作者：

Benzahi, Ahlem ^{[1
]}

Arar, Nouria ^{[2
]}

Abada, Nadjet ^{[3
]}

Rhaima, Mohamed ^{[4
]}

Mchiri, Lassaad ^{[5
]}

Makhlouf, Abdellatif Ben ^{[6
]}

机构：

[1] Abdelhafid Boussouf Univ Ctr, Ecole Normale Super El Katiba Assia Djebar, Lab Math Appl & Didact MAD, Mila, Constantine, Algeria

[2] Univ Freres Mentouri, Lab Math & Sci Decis LAMASD, Constantine 25017, Algeria

[3] Ecole Normale Super El Katiba Assia Djebar, Lab Math Appl & Didact MAD, Constantine, Algeria

[4] King Saud Univ, Coll Sci, Dept Stat & Operat Res, POB 2455, Riyadh 11451, Saudi Arabia

[5] Univ Evry Val DEssonne, ENSIIE, 1 Sq Resistance, F-91025 Evry Courcouronnes, France

[6] Sfax Univ, Fac Sci, Dept Math, BP 1171, Sfax, Tunisia

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2023年 / 30卷 / 04期

关键词：

Fractional integro-differential equations; Caputo fractional derivative; Chebyshev polynomials; Chebyshev spectral method; Least squares approximation; DIFFUSION;

D O I：

10.1007/s44198-023-00128-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the fractional derivative is considered in the Caputo sense. In this work, the least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) of the first Kind is applied to solving a class of FIDEs. Our aim is to write the unknown function as a series of a linear combination of SCP, and then to reduce the problem to a system of linear algebraic equations, which will be solved for the unknown constants associated with the approximate solution, using MATLAB R2020a. Finally, numerical examples are presented to confirm the reliability, applicability, and efficiency of this method, in addition, various comparisons are also shown.

引用

页码：1392 / 1408

页数：17

共 50 条

[21] Semilinear fractional integro-differential equations with compact semigroup
Rashid, M. H. M.
El-Qaderi, Yahya
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : 6276 - 6282
[22] Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space
Alsa'di, K.
Long, N. M. A. Nik
Eshkuvatov, Z. K.
MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, 2024, 18 (03): : 469 - 489
[23] Chebyshev cardinal functions: An effective tool for solving nonlinear Volterra and Fredholm integro-differential equations of fractional order
Irandoust-pakchin, S.
Kheiri, H.
Abdi-mazraeh, S.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2013, 37 (A1): : 53 - 62
[24] An efficient numerical method based on ultraspherical polynomials for linear weakly singular fractional Volterra integro-differential equations
Sajjadi, Sayed Arsalan
Saberi Najafi, Hashem
Aminikhah, Hossein
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (12) : 10293 - 10308
[25] NUMERICAL TREATMENT OF VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER AND ITS CONVERGENCE ANALYSIS
Panda, Abhilipsa
Mohapatra, Jugal
KRAGUJEVAC JOURNAL OF MATHEMATICS, 2025, 49 (04): : 615 - 637
[26] Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations
Doha, E. H.
Abdelkawy, M. A.
Amin, A. Z. M.
Lopes, Antonio M.
ENGINEERING WITH COMPUTERS, 2022, 38 (SUPPL 2) : 1363 - 1373
[27] An Analytical Numerical Method for Solving Fuzzy Fractional Volterra Integro-Differential Equations
Alaroud, Mohammad
Al-Smadi, Mohammed
Ahmad, Rokiah Rozita
Din, Ummul Khair Salma
SYMMETRY-BASEL, 2019, 11 (02):
[28] Fractional Bell collocation method for solving linear fractional integro-differential equations
Yuzbasi, Suayip
MATHEMATICAL SCIENCES, 2024, 18 (01) : 29 - 40
[29] Numerical solution of Volterra-Fredholm integral equations by moving least square method and Chebyshev polynomials
Dastjerdi, H. Laeli
Ghaini, F. M. Maalek
APPLIED MATHEMATICAL MODELLING, 2012, 36 (07) : 3277 - 3282
[30] An approach based on fractional-order Lagrange polynomials for the numerical approximation of fractional order non-linear Volterra-Fredholm integro-differential equations
Saurabh Kumar
Vikas Gupta
Journal of Applied Mathematics and Computing, 2023, 69 : 251 - 272

← 1 2 3 4 5 →