| Summary: | �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:
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