Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi Polynomials
The Genocchi polynomial has been increasingly used as a convenient tool to solve some fractional calculus problems, due to their nice properties. However, like some other members in the Appell polynomials, the nice properties are always limited to the interval defined in ½0, 1�. In this paper, we ex...
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Hindawi
2023
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| Online Access: | http://eprints.uthm.edu.my/9593/ http://eprints.uthm.edu.my/9593/1/J16109_345440b6eeae9092d304a148e11323b2.pdf |
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| author | Jian Rong Loh, Jian Rong Loh Chang Phang, Chang Phang Abdulnasir Isah, Abdulnasir Isah |
| author_facet | Jian Rong Loh, Jian Rong Loh Chang Phang, Chang Phang Abdulnasir Isah, Abdulnasir Isah |
| author_sort | Jian Rong Loh, Jian Rong Loh |
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| description | The Genocchi polynomial has been increasingly used as a convenient tool to solve some fractional calculus problems, due to their nice properties. However, like some other members in the Appell polynomials, the nice properties are always limited to the interval defined in ½0, 1�. In this paper, we extend the Genocchi polynomials to the general shifted Genocchi polynomials, Sða,bÞ n ðxÞ, which are defined for interval ½a, b�. New properties for this general shifted Genocchi polynomials will be introduced, including the determinant form. This general shifted Genocchi polynomials can overcome the conventional formula of finding
the Genocchi coefficients of a function fðxÞ that involves f ðn−1Þ ðxÞ which may not be defined at x = 0, 1. Hence, we use the general shifted Genocchi polynomials to derive the operational matrix and hence to solve the Fredholm-type fractional integrodifferential equations with arbitrary domain ½a, b�. |
| first_indexed | 2025-11-15T20:30:39Z |
| format | Article |
| id | uthm-9593 |
| institution | Universiti Tun Hussein Onn Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:30:39Z |
| publishDate | 2023 |
| publisher | Hindawi |
| recordtype | eprints |
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| spelling | uthm-95932023-08-07T02:26:12Z http://eprints.uthm.edu.my/9593/ Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi Polynomials Jian Rong Loh, Jian Rong Loh Chang Phang, Chang Phang Abdulnasir Isah, Abdulnasir Isah T Technology (General) The Genocchi polynomial has been increasingly used as a convenient tool to solve some fractional calculus problems, due to their nice properties. However, like some other members in the Appell polynomials, the nice properties are always limited to the interval defined in ½0, 1�. In this paper, we extend the Genocchi polynomials to the general shifted Genocchi polynomials, Sða,bÞ n ðxÞ, which are defined for interval ½a, b�. New properties for this general shifted Genocchi polynomials will be introduced, including the determinant form. This general shifted Genocchi polynomials can overcome the conventional formula of finding the Genocchi coefficients of a function fðxÞ that involves f ðn−1Þ ðxÞ which may not be defined at x = 0, 1. Hence, we use the general shifted Genocchi polynomials to derive the operational matrix and hence to solve the Fredholm-type fractional integrodifferential equations with arbitrary domain ½a, b�. Hindawi 2023 Article PeerReviewed text en http://eprints.uthm.edu.my/9593/1/J16109_345440b6eeae9092d304a148e11323b2.pdf Jian Rong Loh, Jian Rong Loh and Chang Phang, Chang Phang and Abdulnasir Isah, Abdulnasir Isah (2023) Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi Polynomials. Journal of Function Spaces. pp. 1-12. https://doi.org/10.1155/2023/5921425 |
| spellingShingle | T Technology (General) Jian Rong Loh, Jian Rong Loh Chang Phang, Chang Phang Abdulnasir Isah, Abdulnasir Isah Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi Polynomials |
| title | Numerical Solution for Arbitrary Domain of Fractional
Integro-differential Equation via the General Shifted
Genocchi Polynomials |
| title_full | Numerical Solution for Arbitrary Domain of Fractional
Integro-differential Equation via the General Shifted
Genocchi Polynomials |
| title_fullStr | Numerical Solution for Arbitrary Domain of Fractional
Integro-differential Equation via the General Shifted
Genocchi Polynomials |
| title_full_unstemmed | Numerical Solution for Arbitrary Domain of Fractional
Integro-differential Equation via the General Shifted
Genocchi Polynomials |
| title_short | Numerical Solution for Arbitrary Domain of Fractional
Integro-differential Equation via the General Shifted
Genocchi Polynomials |
| title_sort | numerical solution for arbitrary domain of fractional
integro-differential equation via the general shifted
genocchi polynomials |
| topic | T Technology (General) |
| url | http://eprints.uthm.edu.my/9593/ http://eprints.uthm.edu.my/9593/ http://eprints.uthm.edu.my/9593/1/J16109_345440b6eeae9092d304a148e11323b2.pdf |