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Systems of Nonlinear Fractional Differential Equations

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Published/Copyright: February 10, 2015
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 18 Issue 1

Abstract

Using the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives $D^{q}_{T}x$ and $D^{q}_{T}y$. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.

MSC 2010: 26A33; 34A12; 34A30; 34A34
Key Words and Phrases: systems of fractional differential equations; iterative method; existence of solutions; Mittag-Leffler type functions

References

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Received: 2014-4-17
Published Online: 2015-2-10

© 2015 Diogenes Co., Sofia

Articles in the same Issue

  1. FCAA Related News, Events and Books (FCAA-Volume 18-1-2015)
  2. Electrolytic Fractional Derivative and Integral of Two-Terminal Element
  3. Initial Value Problem of Fractional Integro-Differential Equations in Banach Space
  4. Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation
  5. Multiple Solutions for a Class of Fractional Hamiltonian Systems
  6. Some Analytical and Numerical Properties of the Mittag-Leffler Functions
  7. Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
  8. Systems of Nonlinear Fractional Differential Equations
  9. Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian
  10. Invariant Subspace Method and Exact Solutions of Certain Nonlinear Time Fractional Partial Differential Equations
  11. Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions
  12. New Stability Results for Partial Fractional Differential Inclusions with Not Instantaneous Impulses
  13. Several Results of Fractional Derivatives in Dʹ(R+)
  14. Modeling Extreme-Event Precursors with the Fractional Diffusion Equation
  15. Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence
  16. Improvements on Flat Output Characterization for Fractional Systems
  17. Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions
  18. Remarks to the Paper “On the Existence of Blow UP Solutions for a Class of Fractional Differential Equations” by Z. Bai et al., In “FCAA”, VOL. 17, NO 4 (2014), 1175-1187
https://doi.org/10.1515/fca-2015-0008
Keywords for this article
systems of fractional differential equations; iterative method; existence of solutions; Mittag-Leffler type functions

Articles in the same Issue

  1. FCAA Related News, Events and Books (FCAA-Volume 18-1-2015)
  2. Electrolytic Fractional Derivative and Integral of Two-Terminal Element
  3. Initial Value Problem of Fractional Integro-Differential Equations in Banach Space
  4. Examples of Analytical Solutions by Means of Mittag-Leffler Function of Fractional Black-Scholes Option Pricing Equation
  5. Multiple Solutions for a Class of Fractional Hamiltonian Systems
  6. Some Analytical and Numerical Properties of the Mittag-Leffler Functions
  7. Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions
  8. Systems of Nonlinear Fractional Differential Equations
  9. Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian
  10. Invariant Subspace Method and Exact Solutions of Certain Nonlinear Time Fractional Partial Differential Equations
  11. Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions
  12. New Stability Results for Partial Fractional Differential Inclusions with Not Instantaneous Impulses
  13. Several Results of Fractional Derivatives in Dʹ(R+)
  14. Modeling Extreme-Event Precursors with the Fractional Diffusion Equation
  15. Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence
  16. Improvements on Flat Output Characterization for Fractional Systems
  17. Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions
  18. Remarks to the Paper “On the Existence of Blow UP Solutions for a Class of Fractional Differential Equations” by Z. Bai et al., In “FCAA”, VOL. 17, NO 4 (2014), 1175-1187
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