Studies in fractal–fractional operators with examples
By using the generalization of the gamma function (p-gamma function: Γp(.)), we introduce a generalization of the fractal–fractional calculus which is called p-fractal fractional calculus. We extend the proposed operators into the symmetric complex domain, specifically the open unit disk. Normalizat...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X24000144 |
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| author | Rabha W. Ibrahim |
| author_facet | Rabha W. Ibrahim |
| author_sort | Rabha W. Ibrahim |
| collection | DOAJ |
| description | By using the generalization of the gamma function (p-gamma function: Γp(.)), we introduce a generalization of the fractal–fractional calculus which is called p-fractal fractional calculus. We extend the proposed operators into the symmetric complex domain, specifically the open unit disk. Normalization for each operator is formulated. This allows us to explore the most important geometric properties. Examples are illustrated including the basic power functions. |
| format | Article |
| id | doaj-art-53cba14cd326438d9df9e14992303855 |
| institution | OA Journals |
| issn | 2666-657X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-53cba14cd326438d9df9e149923038552025-08-20T01:58:16ZengElsevierExamples and Counterexamples2666-657X2024-12-01610014810.1016/j.exco.2024.100148Studies in fractal–fractional operators with examplesRabha W. Ibrahim0Correspondence to: Istanbul Okan University, Faculty of Engineering and Natural Sciences, Advanced Computing Lab, Turkey.; Istanbul Okan University,Faculty of Engineering and Natural Sciences, Advanced Computing Lab, Turkey; Information and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar, IraqBy using the generalization of the gamma function (p-gamma function: Γp(.)), we introduce a generalization of the fractal–fractional calculus which is called p-fractal fractional calculus. We extend the proposed operators into the symmetric complex domain, specifically the open unit disk. Normalization for each operator is formulated. This allows us to explore the most important geometric properties. Examples are illustrated including the basic power functions.http://www.sciencedirect.com/science/article/pii/S2666657X24000144Fractional calculusFractal calculusFractional difference operatorFractal–fractional differential operator |
| spellingShingle | Rabha W. Ibrahim Studies in fractal–fractional operators with examples Examples and Counterexamples Fractional calculus Fractal calculus Fractional difference operator Fractal–fractional differential operator |
| title | Studies in fractal–fractional operators with examples |
| title_full | Studies in fractal–fractional operators with examples |
| title_fullStr | Studies in fractal–fractional operators with examples |
| title_full_unstemmed | Studies in fractal–fractional operators with examples |
| title_short | Studies in fractal–fractional operators with examples |
| title_sort | studies in fractal fractional operators with examples |
| topic | Fractional calculus Fractal calculus Fractional difference operator Fractal–fractional differential operator |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X24000144 |
| work_keys_str_mv | AT rabhawibrahim studiesinfractalfractionaloperatorswithexamples |