%0 Journal Article %T Dual identities in fractional difference calculus within Riemann %A T. Abdeljawad %J Adv. Difference Equ. %D 2013 %V 2013 %F Abdeljawad2013 %0 Journal Article %T On delta and nabla Caputo fractional differences and dual identities %A T. Abdeljawad %J Discrete Dyn. Nat. Soc. %D 2013 %V 2013 %F Abdeljawad2013 %0 Journal Article %T On conformable fractional calculus %A T. Abdeljawad %J J. Comput. Appl. Math. %D 2015 %V 279 %F Abdeljawad2015 %0 Journal Article %T On the definitions of nabla fractional operators %A T. Abdeljawad %A F. M. Atici %J Abstr. Appl. Anal. %D 2012 %V 2012 %F Abdeljawad2012 %0 Journal Article %T Fractional differences and integration by parts %A T. Abdeljawad %A D. Baleanu %J J. Comput. Anal. Appl. %D 2011 %V 13 %F Abdeljawad2011 %0 Journal Article %T Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels %A T. Abdeljawad %A D. Baleanu %J Adv. Difference Equ. %D 2016 %V 2016 %F Abdeljawad2016 %0 Journal Article %T Formulation of Euler-Lagrange equations for fractional variational problems %A O. P. Agrawal %J J. Math. Anal. Appl. %D 2002 %V 272 %F Agrawal2002 %0 Journal Article %T Chua’s circuit model with Atangana-Baleanu derivative with fractional order %A B. S. T. Alkahtani %J Chaos Solitons Fractals %D 2016 %V 89 %F Alkahtani2016 %0 Journal Article %T New fractional derivative with non-local and non-singular kernel: theory and application to heat transfer model %A A. Atangana %A D. Baleanu %J Therm. Sci. %D 2016 %V 20 %F Atangana2016 %0 Journal Article %T Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order %A A. Atangana %A I. Koca %J Chaos Solitons Fractals %D 2016 %V 89 %F Atangana2016 %0 Journal Article %T On exact solutions of a class of fractional Euler-Lagrange equations %A D. Baleanu %A J. J. Trujillo %J Nonlinear Dynam. %D 2008 %V 52 %F Baleanu2008 %0 Journal Article %T A new definition of fractional derivative without singular kernel %A M. Caputo %A M. Fabrizio %J Progr. Fract. Differ. Appl. %D 2015 %V 1 %F Caputo2015 %0 Journal Article %T Fractional Maxwell fluid with fractional derivative without singular kernel %A F. Gao %A X.-J. Yang %J Therm. Sci. %D 2016 %V 20 %F Gao2016 %0 Book %T Applications of fractional calculus in physics %A R. Hilfer %D 2000 %I World Sci. Publ. %C Singapore %F Hilfer 2000 %0 Journal Article %T A new definition of fractional derivative %A R. Khalil %A M. Al Horani %A A. Yousef %A M. Sababheh %J J. Comput. Appl. Math. %D 2014 %V 264 %F Khalil2014 %0 Journal Article %T Generalized Mittag-Leffler function and generalized fractional calculus operators %A A. A. Kilbas %A M. Saigo %A K. Saxena %J Integral Transforms Spec. Funct. %D 2004 %V 15 %F Kilbas2004 %0 Book %T Theory and applications of fractional differential equations %A A. A. Kilbas %A H. M. Srivastava %A J. J. Trujillo %D 2006 %I North-Holland Mathematics Studies, Elsevier Science B.V. %C Amsterdam %F Kilbas2006 %0 Journal Article %T Variable order and distributed order fractional operators %A C. F. Lorenzo %A T. T. Hartley %J Fractional order calculus and its applications, Nonlinear Dynam. %D 2002 %V 29 %F Lorenzo2002 %0 Journal Article %T Properties of a new fractional derivative without singular kernel %A J. Losada %A J. J. Nieto %J Progr. Fract. Differ. Appl. %D 2015 %V 1 %F Losada2015 %0 Journal Article %T Recent history of fractional calculus %A J. T. Machado %A V. Kiryakova %A F. Mainardi %J Commun. Nonlinear Sci. Numer. Simul. %D 2011 %V 16 %F Machado2011 %0 Book %T Fractional calculus in bioengineering %A R. L. Magin %D 2006 %I Begell House Publishers Inc. %C CT %F Magin2006 %0 Journal Article %T Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives %A T. Maraaba %A D. Baleanu %A F. Jarad %J J. Math. Phys. %D 2008 %V 49 %F Maraaba2008 %0 Book %T Fractional differential equations %A I. Podlubny %D 1999 %I An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in Science and Engineering, Academic Press, Inc. %C San Diego, CA %F Podlubny1999 %0 Book %T Fractional integrals and derivatives %A S. G. Samko %A A. A. Kilbas %A O. I. Marichev %D 1993 %I Theory and applications, Edited and with a foreword by S. M. Nikol’ski˘ı, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers %C Yverdon %F Samko1993 %0 Book %T Local fractional integral transforms and their applications %A X.-J. Yang %A D. Baleanu %A H. M. Srivastava %D 2005 %I Elsevier/Academic Press %C Amsterdam %F Yang2005 %0 Journal Article %T On steady heat flow problem involving Yang-Srivastava-Machado fractional derivative without singular kernel %A A.-M. Yang %A Y. Han %A J. Li %A W.-X. Liu %J Therm. Sci. %D 2016 %V 20 %F Yang2016 %0 Journal Article %T A new fractional derivative without singular kernel: application to the modelling of the steady heat flow %A X.-J. Yang %A H. M. Srivastava %A J. A. Tenreiro Machado %J Therm. Sci. %D 2016 %V 20 %F Yang2016