Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations

Md Nasrudin, Farah Suraya and Chang Phang, Chang Phang (2022) Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations. Journal of Mathematics and Statistics, 2022. pp. 1-7. ISSN 1549-3644

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Abstract

�e operational matrix method is one of the powerful tools for solving fractional di�erential equations. �is method uses the concept of replacing a symbol with another symbol, i.e., replacing symbol fractional derivative, Dα, with another symbol, which is an operational matrix, Pα. In [1], the authors had derived shifted Legendre operational matrix for solving fractional di�erential equations, de�ned in Caputo sense. �en, researchers started to apply the various types of poly�nomials to derive the operational matrix for solving various types of fractional calculus problems, including Genocchi operational matrix for fractional partial di�erential equations [2], Laguerre polynomials operational matrix for solving fractional di�erential equations with non-singular kernel [3], and Mu¨ntz–Legendre polynomial operational matrix for solving distributed order fractional di�erential equations [4] Recently, apart from the fractional di�erential equation de�ned in Caputo sense, this kind of operational matrix method had been extended to tackle another type of frac�tional derivative or operator, which includes the Caputo–Fabrizio operator [5] and Atangana–Baleanu de�rivative [6, 7]. In this research direction, the operational matrix method is either an operational matrix of derivative or operational matrix of integration based on certain polynomials. �e operational matrix method is possible to apply to another type of fractional derivatives if there is an analytical expression for xp (where p is integer positive) in the sense of certain fractional derivatives or operators. Hence, we extend this operational matrix to tackle operator de�ned by one parameter Mittag–Le�er function, i.e. Antagana–Baleunu derivative [6] to the operator that de- �ned by using three-parameter Mittag–Le�er function, so�called Prabhakar fractional integrals or derivative. In short, we aim to solve the following fractional di�erential equation defined in Prabhakar sense:

Item Type:	Article
Subjects:	T Technology > T Technology (General)
Depositing User:	Mr. Abdul Rahim Mat Radzuan
Date Deposited:	21 Jul 2022 03:50
Last Modified:	21 Jul 2022 03:50
URI:	http://eprints.uthm.edu.my/id/eprint/7295

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