NUMERICAL ANALYSIS OF SOME FRACTIONAL ORDER DIFFERENTIAL EQUATIONS VIA LEGENDRE SPECTRAL METHOD

Aziz Khan (), Hafsa Naz (), Muhammad Sarwar (), Kamal Shah, Manar A. Alqudah () and Thabet Abdeljawad
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Aziz Khan: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Hafsa Naz: Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000 Khyber Pakhtunkhwa, Pakistan
Muhammad Sarwar: Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000 Khyber Pakhtunkhwa, Pakistan
Kamal Shah: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia2Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000 Khyber Pakhtunkhwa, Pakistan
Manar A. Alqudah: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia4Department of Medical Research, China Medical University, Taichung 40402, Taiwan5Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-13

Abstract: In this research paper, we find the numerical solutions of fractional order scalers and coupled system of differential equations under initial conditions using shifted Legendre polynomials. By using the properties of shifted Legendre polynomials, we establish operational matrices of integration and differentiation in order to simplify our considered problems under initial conditions. In order to check the accuracy of the proposed model, some test problems are solved along with the graphical representations. For coupled system, we applied the algorithm to the Pharmacokinetic two-compartment model. As the proposed method is computer-oriented, we use therefore the MATLAB for required calculations. Numerical results are shown graphically.

Keywords: Operational Matrices; Shifted Legendre Polynomials; Fractional Order Differential Equations; Initial Conditions; Pharmacokinetic Two-Compartment Model; Scaler Problem; Coupled System (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400364

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