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Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions

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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

We study a class of fractional integro-differential inclusions with integral boundary conditions and establish a Filippov type existence result in the case of nonconvex set-valued maps.

MSC 2010: Primary 34A60; Secondary 34A08
Key Words and Phrases: differential inclusion; fractional derivative; boundary value problem

References

[1] A. Aghajani, Y. Jalilian, J. J. Trujillo, On the existence of solutions of fractional integro-differential equations. Fract. Calc. Appl. Anal. 15, No 1 (2012), 44-69; DOI: 10.2478/s13540-012-0005-4; http://link.springer.com/article/10.2478/s13540-012-0005-4.Search in Google Scholar

[2] B. Ahmad, S. K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012), 362-382; DOI: 10.2478/s13540-012-0027-y; http://link.springer.com/article/10.2478/s13540-012-0027-y.10.2478/s13540-012-0027-ySearch in Google Scholar

[3] B. Ahmad, S. K. Ntouyas, A. Alsaedi, New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions. Boundary Value Problems2013 (2013), Paper No 275, 14 p.10.1186/1687-2770-2013-275Search in Google Scholar

[4] B. Ahmad, S. K. Ntouyas, A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Fract. Calc. Appl. Anal. 17, No 2 (2014), 348-360; DOI: 10.2478/s13540-014-0173-5; http://link.springer.com/article/10.2478/s13540-014-0173-5.Search in Google Scholar

[5] J. P. Aubin, H. Frankowska, Set-valued Analysis. Birkhauser, Basel (1990).Search in Google Scholar

[6] A. F. Filippov, Classical solutions of differential equations with multivalued right hand side. SIAM J. Control5 (1967), 609-621.10.1137/0305040Search in Google Scholar

[7] J. Hadamard, Essai sur l'etude des fonctions donnees par leur development de Taylor. J. Math. Pures Appl. 8 (1892), 101-186.Search in Google Scholar

[8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).Search in Google Scholar

[9] A. A. Kilbas, Hadamard-type fractional calculus. J. Korean Math. Soc. 38 (2001), 1191-1204.Search in Google Scholar

Received: 2014-6-5
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-2015-0011
Keywords for this article
differential inclusion; fractional derivative; boundary value problem

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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