New technique for solving the numerical computation of neutral fractional functional integro-differential equation based on the Legendre wavelet method

Kanagaraj Muthuselvan; Baskar Sundaravadivoo; Kottakkaran Sooppy Nisar; Fahad Sameer Alshammari; Kanagaraj Muthuselvan; Baskar Sundaravadivoo; Kottakkaran Sooppy Nisar; Fahad Sameer Alshammari

doi:10.3934/math.2024694

AIMS Mathematics

2024, Volume 9, Issue 6: 14288-14309. doi: 10.3934/math.2024694

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New technique for solving the numerical computation of neutral fractional functional integro-differential equation based on the Legendre wavelet method

1.
Department of Mathematics, Alagappa University, Karaikudi 630004, Tamil Nadu, India
2.
Department of Mathematics, Central University of Tamil Nadu, Thiruvarur 610005, India
3.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
4.
Saveetha School of Engineering, SIMATS, Chennai, India

Received: 15 February 2024 Revised: 04 April 2024 Accepted: 08 April 2024 Published: 19 April 2024
MSC : 42C10, 34K37, 34K40

The aim of this work is to solve a numerical computation of the neutral fractional functional integro-differential equation based on a new approach to the Legendre wavelet method. The concept of fractional derivatives was examined in the sense of Caputo. The properties of the Legendre wavelet and function approximation were employed to determine the approximate solution of a given dynamical system. Moreover, the error estimations and convergence analysis of the truncated Legendre wavelet expansion for the proposed problem were discussed. The validity and applicability of this proposed technique to numerical computation were shown by illustrative examples. Eventually, the results of this technique demonstrate its great effectiveness and reliability.
- fractional derivatives,
- Legendre wavelet,
- numerical computation,
- error analysis
Citation: Kanagaraj Muthuselvan, Baskar Sundaravadivoo, Kottakkaran Sooppy Nisar, Fahad Sameer Alshammari. New technique for solving the numerical computation of neutral fractional functional integro-differential equation based on the Legendre wavelet method[J]. AIMS Mathematics, 2024, 9(6): 14288-14309. doi: 10.3934/math.2024694

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Abstract

The aim of this work is to solve a numerical computation of the neutral fractional functional integro-differential equation based on a new approach to the Legendre wavelet method. The concept of fractional derivatives was examined in the sense of Caputo. The properties of the Legendre wavelet and function approximation were employed to determine the approximate solution of a given dynamical system. Moreover, the error estimations and convergence analysis of the truncated Legendre wavelet expansion for the proposed problem were discussed. The validity and applicability of this proposed technique to numerical computation were shown by illustrative examples. Eventually, the results of this technique demonstrate its great effectiveness and reliability.

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