-Dimensional Fractional Lagrange's Inversion Theorem
Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for on...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/310679 |
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| author | F. A. Abd El-Salam |
| author_facet | F. A. Abd El-Salam |
| author_sort | F. A. Abd El-Salam |
| collection | DOAJ |
| description | Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved. |
| format | Article |
| id | doaj-art-09bd50b072604bd7bc2168a057cb279f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-09bd50b072604bd7bc2168a057cb279f2025-02-03T06:14:17ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/310679310679-Dimensional Fractional Lagrange's Inversion TheoremF. A. Abd El-Salam0Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah, Saudi ArabiaUsing Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.http://dx.doi.org/10.1155/2013/310679 |
| spellingShingle | F. A. Abd El-Salam -Dimensional Fractional Lagrange's Inversion Theorem Abstract and Applied Analysis |
| title | -Dimensional Fractional Lagrange's Inversion Theorem |
| title_full | -Dimensional Fractional Lagrange's Inversion Theorem |
| title_fullStr | -Dimensional Fractional Lagrange's Inversion Theorem |
| title_full_unstemmed | -Dimensional Fractional Lagrange's Inversion Theorem |
| title_short | -Dimensional Fractional Lagrange's Inversion Theorem |
| title_sort | dimensional fractional lagrange s inversion theorem |
| url | http://dx.doi.org/10.1155/2013/310679 |
| work_keys_str_mv | AT faabdelsalam dimensionalfractionallagrangesinversiontheorem |