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Numerical Analysis Of Some Fractional Order Differential Equations Via Legendre Spectral Method

Author

Listed:
  • 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)

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.

Suggested Citation

  • Aziz Khan & Hafsa Naz & Muhammad Sarwar & Kamal Shah & Manar A. Alqudah & Thabet Abdeljawad, 2023. "Numerical Analysis Of Some Fractional Order Differential Equations Via Legendre Spectral Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400364
    DOI: 10.1142/S0218348X23400364
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