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 0,1. In this paper, we exten...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/5921425 |
| _version_ | 1797814561473036288 |
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| author | Jian Rong Loh Chang Phang Abdulnasir Isah |
| author_facet | Jian Rong Loh Chang Phang Abdulnasir Isah |
| author_sort | Jian Rong Loh |
| collection | DOAJ |
| 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 0,1. In this paper, we extend the Genocchi polynomials to the general shifted Genocchi polynomials, Sna,bx, which are defined for interval a,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 fx that involves fn−1x 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 integro-differential equations with arbitrary domain a,b. |
| first_indexed | 2024-03-13T08:09:29Z |
| format | Article |
| id | doaj.art-7f38b284be2a41728bd178d4be1e40ba |
| institution | Directory Open Access Journal |
| issn | 2314-8888 |
| language | English |
| last_indexed | 2024-03-13T08:09:29Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj.art-7f38b284be2a41728bd178d4be1e40ba2023-06-01T00:00:03ZengHindawi LimitedJournal of Function Spaces2314-88882023-01-01202310.1155/2023/5921425Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi PolynomialsJian Rong Loh0Chang Phang1Abdulnasir Isah2Foundation in EngineeringDepartment of Mathematics and StatisticsDepartment of Mathematics EducationThe 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 0,1. In this paper, we extend the Genocchi polynomials to the general shifted Genocchi polynomials, Sna,bx, which are defined for interval a,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 fx that involves fn−1x 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 integro-differential equations with arbitrary domain a,b.http://dx.doi.org/10.1155/2023/5921425 |
| spellingShingle | Jian Rong Loh Chang Phang Abdulnasir Isah Numerical Solution for Arbitrary Domain of Fractional Integro-differential Equation via the General Shifted Genocchi Polynomials Journal of Function Spaces |
| 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 |
| url | http://dx.doi.org/10.1155/2023/5921425 |
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