John Graef

Prof. John Graef

Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
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Research Focus & Metrics

Academic Career Length

29Years (1998-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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1 July 2008 in Applicable Analysis
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Journal Article
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MBMouffak Benchohra
Mouffak Benchohra
John GraefJohn Graef
John Graef
SHSamira Hamani
Samira Hamani
In this article, the authors establish sufficient conditions for the existence of solutions to a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative of order α ∈ (1, 2] and non-linear integral conditions.

13 November 2012 in Journal of Mathematical Sciences
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BBBaculíková Blanka
Baculíková Blanka
JDJozef Džurina
Jozef Džurina
John GraefJohn Graef
John Graef

21 March 2014 in Fractional Calculus and Applied Analysis
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Journal Article
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John GraefJohn Graef
John Graef
Lingju KongLingju Kong
Lingju Kong
MWMin Wang
Min Wang
In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

2 March 2012 in Results in Mathematics
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John GraefJohn Graef
John Graef
SHShapour Heidarkhani
Shapour Heidarkhani
LKLingju Kong
Lingju Kong

1 February 2012 in Computers & Mathematics with Applications
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Journal Article
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SGSaid R. Grace
Said R. Grace
John GraefJohn Graef
John Graef
Mohamed El-BeltagyMohamed El-Beltagy
Mohamed El-Beltagy

6 June 2014 in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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John GraefJohn Graef
John Graef
Cemil TunçCemil Tunç
Cemil Tunç