Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations
In this work, we apply the operational matrix based on shifted Legendre polynomials for solving Prabhakar fractional differential equations. The Prabhakar derivative is defined in three-parameter Mittag-Leffler function. We achieve this by first deriving the analytical expression for Prabhakar deriv...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7220433 |
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| author | Farah Suraya Md Nasrudin Chang Phang |
| author_facet | Farah Suraya Md Nasrudin Chang Phang |
| author_sort | Farah Suraya Md Nasrudin |
| collection | DOAJ |
| description | In this work, we apply the operational matrix based on shifted Legendre polynomials for solving Prabhakar fractional differential equations. The Prabhakar derivative is defined in three-parameter Mittag-Leffler function. We achieve this by first deriving the analytical expression for Prabhakar derivative of xp where p is positive integer, via integration. Hence, for the first time, the operational matrix method for Prabhakar derivative is derived by using the properties of shifted Legendre polynomials. Hence, we transform the Prabhakar fractional differential equations into a system of algebraic equations. By solving the system of algebraic equations, we were able to obtain the numerical solution of fractional differential equations defined in Prabhakar derivative. Only a few terms of shifted Legendre polynomials are needed for achieving the accurate solution. |
| format | Article |
| id | doaj-art-d146c3fe0fa5462486d442d5a150f9f5 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d146c3fe0fa5462486d442d5a150f9f52025-02-03T01:07:37ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7220433Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential EquationsFarah Suraya Md Nasrudin0Chang Phang1Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsIn this work, we apply the operational matrix based on shifted Legendre polynomials for solving Prabhakar fractional differential equations. The Prabhakar derivative is defined in three-parameter Mittag-Leffler function. We achieve this by first deriving the analytical expression for Prabhakar derivative of xp where p is positive integer, via integration. Hence, for the first time, the operational matrix method for Prabhakar derivative is derived by using the properties of shifted Legendre polynomials. Hence, we transform the Prabhakar fractional differential equations into a system of algebraic equations. By solving the system of algebraic equations, we were able to obtain the numerical solution of fractional differential equations defined in Prabhakar derivative. Only a few terms of shifted Legendre polynomials are needed for achieving the accurate solution.http://dx.doi.org/10.1155/2022/7220433 |
| spellingShingle | Farah Suraya Md Nasrudin Chang Phang Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations Journal of Mathematics |
| 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 |
| url | http://dx.doi.org/10.1155/2022/7220433 |
| work_keys_str_mv | AT farahsurayamdnasrudin numericalsolutionviaoperationalmatrixforsolvingprabhakarfractionaldifferentialequations AT changphang numericalsolutionviaoperationalmatrixforsolvingprabhakarfractionaldifferentialequations |