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Nonlocal boundary value problems for Hilfer fractional differential equations

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In this paper, we initiate the study of boundary value problems involving Hilfer fractional derivatives. Several new existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating our results are also presented.

Abstract

In this paper, we initiate the study of boundary value problems involving Hilfer fractional derivatives. Several new existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating our results are also presented.

참고문헌 (16)

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  5. H. Gu, "Existence of mild solution for evolution equation with Hilfer fractional derivative", Appl. Math. Comput, 257, pp.344~354 (2015)
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  9. A. A. Kilbas, "Theory and Applications of the Fractional Differential Equations", North-Holland Mathematics Studies, 204 (2006), Elsevier Science B.V.
  10. M. A. Krasnoselski, "Two remarks on the method of successive approximations", Uspehi Mat. Nauk (N.S.), 10(1)통권 : 63, pp.123~127 (1955)
  11. V. Lakshmikantham, "Theory of Fractional Dynamic Systems" (2009), Cambridge Scientific Publishers
  12. K. S. Miller, "An Introduction to the Fractional Calculus and Differential Equations" (1993), A Wiley-Interscience Publication, John Wiley & Sons, Inc.
  13. I. Podlubny, "Fractional Differential Equations" (1999), Academic Press, Inc.
  14. S. G. Samko, "Fractional Integrals and Derivatives" (1993), Gordon and Breach Science Publishers
  15. J. Wang, "Nonlocal initial value problems for differential equations with Hilfer fractional derivative", Appl. Math. Comput, 266, pp.850~859 (2015)
  16. Y. Zhou, "Basic Theory of Fractional Differential Equations" (2014), World Scientific Publishing Co. Pte. Ltd.

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