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On Hadamard fractional integro-differential boundary value problems

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Abstract

In this paper, we study the existence and uniqueness of solutions for a fractional integral boundary value problem involving Hadamard type fractional differential equations and integral boundary conditions. Our results are new in the present configuration and are based on some classical ideas of fixed point theory. The paper concludes with some illustrative examples.

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References

  1. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  2. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V, Amsterdam (2006)

    Google Scholar 

  3. Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston (2012)

    MATH  Google Scholar 

  4. Agarwal, R.P., Zhou, Y., He, Y.: Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59, 1095–1100 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Baleanu, D., Mustafa, O.G., Agarwal, R.P.: On L\(^p\)-solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 218, 2074–2081 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ahmad, B., Nieto, J.J.: Riemann–Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl. 36, 9 (2011)

    MathSciNet  Google Scholar 

  7. Ahmad, B., Ntouyas, S.K., Alsaedi, A.: New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ. 2011, 11 (2011). Article ID 107384

    Article  MathSciNet  Google Scholar 

  8. O’Regan, D., Stanek, S.: Fractional boundary value problems with singularities in space variables. Nonlinear Dyn. 71, 641–652 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ahmad, B., Ntouyas, S.K., Alsaedi, A.: A study of nonlinear fractional differential equations of arbitrary order with Riemann–Liouville type multistrip boundary conditions. Math. Probl. Eng. 2013, 9 (2013). Article ID 320415

    MathSciNet  Google Scholar 

  10. Ahmad, B., Nieto, J.J.: Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl. 2013, 8 (2013). Article ID 149659

    Article  MathSciNet  Google Scholar 

  11. Zhang, L., Ahmad, B., Wang, G., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  12. Liu, X., Jia, M., Ge, W.: Multiple solutions of a p-Laplacian model involving a fractional derivative. Adv. Differ. Equ. 2013, 126 (2013)

    Article  MathSciNet  Google Scholar 

  13. Zhong, W., Yang, X., Gao, F.: A Cauchy problem for some local fractional abstract differential equation with fractal conditions. J. Appl. Funct. Anal. 8, 92–99 (2013)

    MATH  MathSciNet  Google Scholar 

  14. Hadamard, J.: Essai sur l’etude des fonctions donnees par leur developpment de Taylor. J. Mat. Pure Appl. Ser. 8, 101–186 (1892)

    MATH  Google Scholar 

  15. Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Compositions of Hadamard-type fractional integration operators and the semigroup property. J. Math. Anal. Appl. 269, 387–400 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Fractional calculus in the Mellin setting and Hadamard-type fractional integrals. J. Math. Anal. Appl. 269, 1–27 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Butzer, P.L., Kilbas, A.A., Trujillo, J.J.: Mellin transform analysis and integration by parts for Hadamard-type fractional integrals. J. Math. Anal. Appl. 270, 1–15 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kilbas, A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38, 1191–1204 (2001)

    MATH  MathSciNet  Google Scholar 

  19. Kilbas, A.A., Trujillo, J.J.: Hadamard-type integrals as G-transforms. Integr. Transform. Spec. Funct. 14, 413–427 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  20. Krasnoselskii, M.A.: Two remarks on the method of successive approximations. Uspekhi Mat. Nauk 10, 123–127 (1955)

    MathSciNet  Google Scholar 

  21. Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)

    Book  MATH  Google Scholar 

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Acknowledgments

The authors are grateful to the anonymous referee for his/her useful comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah , 21589, Saudi Arabia

    Bashir Ahmad

  2. Department of Mathematics, University of Ioannina, 451 10 , Ioannina, Greece

    Sotiris K. Ntouyas

Authors
  1. Bashir Ahmad
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  2. Sotiris K. Ntouyas
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Correspondence to Bashir Ahmad.

Additional information

Bashir Ahmad and Sotiris K. Ntouyas—Member of Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group at King Abdulaziz University, Jeddah, Saudi Arabia.

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Ahmad, B., Ntouyas, S.K. On Hadamard fractional integro-differential boundary value problems. J. Appl. Math. Comput. 47, 119–131 (2015). https://doi.org/10.1007/s12190-014-0765-6

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