Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations
�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 au...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi
2022
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/7295/1/J14305_1eeb3fabff7d91e6857be8589c53a85f%5B1%5D.pdf |
| _version_ | 1825710352346644480 |
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| author | Md Nasrudin, Farah Suraya Chang Phang, Chang Phang |
| author_facet | Md Nasrudin, Farah Suraya Chang Phang, Chang Phang |
| author_sort | Md Nasrudin, Farah Suraya |
| collection | UTHM |
| description | �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: |
| first_indexed | 2024-03-05T21:56:18Z |
| format | Article |
| id | uthm.eprints-7295 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | English |
| last_indexed | 2024-03-05T21:56:18Z |
| publishDate | 2022 |
| publisher | Hindawi |
| record_format | dspace |
| spelling | uthm.eprints-72952022-07-21T03:50:02Z http://eprints.uthm.edu.my/7295/ Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations Md Nasrudin, Farah Suraya Chang Phang, Chang Phang T Technology (General) �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: Hindawi 2022 Article PeerReviewed text en http://eprints.uthm.edu.my/7295/1/J14305_1eeb3fabff7d91e6857be8589c53a85f%5B1%5D.pdf 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 https://doi.org/10.1155/2022/7220433 |
| spellingShingle | T Technology (General) Md Nasrudin, Farah Suraya Chang Phang, Chang Phang Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations |
| title | Numerical Solution via Operational Matrix for Solving Prabhakar
Fractional Differential Equations |
| title_full | Numerical Solution via Operational Matrix for Solving Prabhakar
Fractional Differential Equations |
| title_fullStr | Numerical Solution via Operational Matrix for Solving Prabhakar
Fractional Differential Equations |
| title_full_unstemmed | Numerical Solution via Operational Matrix for Solving Prabhakar
Fractional Differential Equations |
| title_short | Numerical Solution via Operational Matrix for Solving Prabhakar
Fractional Differential Equations |
| title_sort | numerical solution via operational matrix for solving prabhakar fractional differential equations |
| topic | T Technology (General) |
| url | http://eprints.uthm.edu.my/7295/1/J14305_1eeb3fabff7d91e6857be8589c53a85f%5B1%5D.pdf |
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