Solution of fractional integro-differential equations using least squares and shifted legendre methods

• Autorzy: Mahdy Amr M.S. , Nagdy Abbas S. , Mohamed Doaa Sh.

Identyfikatory

DOI

10.17512/jamcm.2024.1.05

• Języki publikacji: EN

Abstrakty

EN

In recent years, fractional calculus (FC) has filled in a hole in traditional calculus in terms of the effect of memory, which lets us know things about the past and present and guess what will happen in the future. It is very important to have this function, especially when studying biological models and integral equations. This paper introduces developed mathematical strategies for understanding a direct arrangement of fractional integro-differential equations (FIDEs). We have presented the least squares procedure and the Legendre strategy for discussing FIDEs. We have given the form of the Caputo concept fractional order operator and the properties. We have presented the properties of the shifted Legendre polynomials. We have shown the steps of the technique to display the solution. Some test examples are given to exhibit the precision and relevance of the introduced strategies. Mathematical outcomes show that this methodology is a comparison between the exact solution and the methods suggested. To show the theoretical results gained, the simulation of suggested strategies is given in eye-catching figures and tables. Program Mathematica 12 was used to get all of the results from the techniques that were shown.

Słowa kluczowe

EN

fractional integro-differential equation; Legendre polynomials; least squares technique; residual equation; weight function; Caputo derivative

PL

ułamkowe równanie całkowo-różniczkowe; wielomiany Legendre'a; równanie resztowe; pochodna Caputo

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 1
• Strony: 59--70
• Opis fizyczny: Bibliogr. 30 poz., tab.

Twórcy

autor

Mahdy Amr M.S.

• Department of Mathematics, Faculty of Science, Zagazig University P.O. Box 44519, Zagazig, Egypt
• Department of Mathematics & Statistics, College of Science Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

autor

Nagdy Abbas S.

• Department of Mathematics, Faculty of Science, Zagazig University P.O. Box 44519, Zagazig, Egypt

autor

Mohamed Doaa Sh.

• Department of Mathematics, Faculty of Science, Zagazig University P.O. Box 44519, Zagazig, Egypt

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).