Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations - Md Nasrudin, Farah Suraya; Chang Phang, Chang Phang (Hindawi, 2022)
e operational matrix method is one of the powerful tools for solving fractional dierential 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 dierential equations, dened in Caputo sense. en, researchers started to apply the various types of polynomials to derive the operational matrix for solving various types of fractional calculus problems, including Genocchi operational matrix for fractional partial dierential equations [2], Laguerre polynomials operational matrix for solving fractional dierential equations with non-singular kernel [3], and Mu¨ntz–Legendre polynomial operational matrix for solving distributed order fractional dierential equations [4] Recently, apart from the fractional dierential equation dened in Caputo sense, this kind of operational matrix method had been extended to tackle another type of fractional derivative or operator, which includes the Caputo–Fabrizio operator [5] and Atangana–Baleanu derivative [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 dened by one parameter Mittag–Leer function, i.e. Antagana–Baleunu derivative [6] to the operator that de- ned by using three-parameter Mittag–Leer function, socalled Prabhakar fractional integrals or derivative. In short, we aim to solve the following fractional dierential equation defined in Prabhakar sense: