@Article{Abdeljawad2013, author="T. Abdeljawad", title="Dual identities in fractional difference calculus within Riemann", journal=" Adv. Difference Equ.", year="2013", pages="16 pages. ", volume="2013" } @Article{Abdeljawad2013, author="T. Abdeljawad", title=" On delta and nabla Caputo fractional differences and dual identities", journal="Discrete Dyn. Nat. Soc.", year="2013", pages="12 pages. ", volume="2013" } @Article{Abdeljawad2015, author="T. Abdeljawad", title=" On conformable fractional calculus", journal=" J. Comput. Appl. Math.", year="2015", pages="57–66. ", volume="279" } @Article{Abdeljawad2012 , author=" T. Abdeljawad, F. M. Atici", title=" On the definitions of nabla fractional operators", journal=" Abstr. Appl. Anal.", year="2012 ", pages="13 pages. ", volume="2012 " } @Article{Abdeljawad2011, author=" T. Abdeljawad, D. Baleanu", title=" Fractional differences and integration by parts", journal=" J. Comput. Anal. Appl.", year="2011", pages=" 574–582.", volume="13" } @Article{Abdeljawad2016, author=" T. Abdeljawad, D. Baleanu", title="Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels", journal="Adv. Difference Equ.", year="2016", pages="18 pages. ", volume="2016" } @Article{Agrawal2002, author="O. P. Agrawal", title=" Formulation of Euler-Lagrange equations for fractional variational problems", journal=" J. Math. Anal. Appl.", year="2002", pages=" 368–379. ", volume="272" } @Article{Alkahtani2016, author="B. S. T. Alkahtani", title=" Chua’s circuit model with Atangana-Baleanu derivative with fractional order", journal="Chaos Solitons Fractals", year="2016", pages=" 547–551. ", volume="89" } @Article{Atangana2016, author="A. Atangana, D. Baleanu", title="New fractional derivative with non-local and non-singular kernel: theory and application to heat transfer model", journal="Therm. Sci.", year="2016", pages="763–769. ", volume="20" } @Article{Atangana2016, author=" A. Atangana, I. Koca", title=" Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order", journal=" Chaos Solitons Fractals", year="2016", pages=" 447–457. ", volume="89" } @Article{Baleanu2008, author="D. Baleanu, J. J. Trujillo", title="On exact solutions of a class of fractional Euler-Lagrange equations", journal="Nonlinear Dynam.", year="2008", pages="331–335.", volume="52" } @Article{Caputo2015, author=" M. Caputo, M. Fabrizio", title=" A new definition of fractional derivative without singular kernel", journal=" Progr. Fract. Differ. Appl.", year="2015", pages=" 73–85. ", volume="1" } @Article{Gao2016, author="F. Gao, X.-J. Yang", title=" Fractional Maxwell fluid with fractional derivative without singular kernel", journal="Therm. Sci.", year="2016", pages="871–877.", volume="20" } @Book{Hilfer 2000, author=" R. Hilfer ", title="Applications of fractional calculus in physics", year="2000", publisher=" World Sci. Publ.", address="Singapore" } @Article{Khalil2014, author="R. Khalil, M. Al Horani, A. Yousef, M. Sababheh", title="A new definition of fractional derivative", journal=" J. Comput. Appl. Math.", year="2014", pages="65–70. ", volume="264" } @Article{Kilbas2004, author="A. A. Kilbas, M. Saigo, K. Saxena", title="Generalized Mittag-Leffler function and generalized fractional calculus operators", journal="Integral Transforms Spec. Funct.", year="2004", pages="31–49. ", volume="15" } @Book{Kilbas2006, author="A. A. Kilbas, H. M. Srivastava, J. J. Trujillo", title="Theory and applications of fractional differential equations", year="2006", publisher="North-Holland Mathematics Studies, Elsevier Science B.V.", address="Amsterdam" } @Article{Lorenzo2002, author="C. F. Lorenzo, T. T. Hartley", title=" Variable order and distributed order fractional operators", journal="Fractional order calculus and its applications, Nonlinear Dynam.", year="2002", pages="57–98. ", volume="29" } @Article{Losada2015, author="J. Losada, J. J. Nieto", title="Properties of a new fractional derivative without singular kernel", journal="Progr. Fract. Differ. Appl.", year="2015", pages="87–92. ", volume="1" } @Article{Machado2011, author="J. T. Machado, V. Kiryakova, F. Mainardi", title="Recent history of fractional calculus", journal="Commun. Nonlinear Sci. Numer. Simul.", year="2011", pages="1140–1153. ", volume="16" } @Book{Magin2006, author="R. L. Magin", title=" Fractional calculus in bioengineering", year="2006", publisher="Begell House Publishers Inc.", address="CT" } @Article{Maraaba2008, author=" T. Maraaba, D. Baleanu, F. Jarad", title="Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives", journal="J. Math. Phys.", year="2008", pages="11 pages. ", volume="49" } @Book{Podlubny1999, author="I. Podlubny", title="Fractional differential equations", year="1999", publisher="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.", address="San Diego, CA" } @Book{Samko1993, author=" S. G. Samko, A. A. Kilbas, O. I. Marichev", title="Fractional integrals and derivatives", year="1993", publisher="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", address="Yverdon" } @Book{Yang2005, author=" X.-J. Yang, D. Baleanu, H. M. Srivastava", title=" Local fractional integral transforms and their applications", year="2005", publisher="Elsevier/Academic Press", address="Amsterdam" } @Article{Yang2016, author=" A.-M. Yang, Y. Han, J. Li, W.-X. Liu", title="On steady heat flow problem involving Yang-Srivastava-Machado fractional derivative without singular kernel", journal="Therm. Sci.", year="2016", pages=" 717–723.", volume="20" } @Article{Yang2016, author="X.-J. Yang, H. M. Srivastava, J. A. Tenreiro Machado", title="A new fractional derivative without singular kernel: application to the modelling of the steady heat flow", journal="Therm. Sci.", year="2016", pages=" 753–756. ", volume="20" }