2012
DOI: 10.1016/j.camwa.2012.01.009
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Existence and uniqueness for a problem involving Hilfer fractional derivative

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Cited by 395 publications
(241 citation statements)
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“…The following is an analogous result to the result for the Riemann-Liouville integral proved in [10].…”
Section: Lemma 18supporting
confidence: 66%
See 1 more Smart Citation
“…The following is an analogous result to the result for the Riemann-Liouville integral proved in [10].…”
Section: Lemma 18supporting
confidence: 66%
“…As for the theory, the investigations include the existence and uniqueness of solutions, asymptotic behavior, stability, etc. See for example the books [1][2][3] and the articles [4][5][6][7][8][9][10] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, Gu and Trujillo [20] reported the existence results of fractional differential equations with Hilfer derivative based on noncompact measure method. The set of two parameters in "Hilfer fractional derivative" ], + of order 0 ≤ ] ≤ 1 and 0 < < 1 permits one to connect between the Caputo and Riemann-Liouville derivatives [17,21,22]. This set of parameters gives an extra degree of freedom on the initial conditions and produces more types of stationary states.…”
Section: Introductionmentioning
confidence: 99%
“…Some properties and applications of the GRLFD are given in [3,4,18,20,21,22]. Several authors (see [2,18,22] [2,18,22,23]. In [23] the authors provided an approach based on the equivalence of a nonlinear Cauchy type problem with GRLFD to a nonlinear Volterra integral equation of the second kind in spaces of summable functions on a finite interval of the real axis and proved uniqueness and existence of the solution, using a variant of the Banach fixed point theorem.…”
Section: Introductionmentioning
confidence: 99%