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N‐Dimensional Fractional Lagrange′s Inversion Theorem

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  • F. A. Abd El-Salam

Abstract

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 N‐dimensional polyadics is derived. A fractional N‐dimensional Lagrange inversion theorem is proved.

Suggested Citation

  • F. A. Abd El-Salam, 2013. "N‐Dimensional Fractional Lagrange′s Inversion Theorem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:310679
    DOI: 10.1155/2013/310679
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    References listed on IDEAS

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    1. Azizollah Babakhani & Dumitru Baleanu, 2012. "Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Azizollah Babakhani & Dumitru Baleanu, 2012. "Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, June.
    3. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, September.
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