@Article{Ahmad2010, author="B. Ahmad, J. J. Nieto", title="Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions", journal="Int. J. Differ. Equ.", year="2010", pages="10 pages", volume="2010" } @Article{Ahmad2012, author="B. Ahmad, J.J. Nieto, A. Alsaedi, M. El-Shahed", title="A study of nonlinear Langevin equation involving two fractional orders in different intervals", journal="Nonlinear Anal. Real World Appl.", year="2012", pages="599--606", volume="13" } @Article{Baghani2017, author="O. Baghani", title="On fractional Langevin equation involving two fractional orders", journal="Commun. Nonlinear Sci. Numer. Simul.", year="2017", pages="675--681", volume="42" } @Article{Baghani2018, author="H. Baghani", title="Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders", journal="J. Fixed Point Theory Appl.", year="2018", pages="7 pages", volume="20" } @Article{Chen2011, author="A. Chen, Y. Chen", title="Existence of Solutions to Nonlinear Langevin Equation Involving Two Fractional Orders with Boundary Value Conditions", journal="Bound. Value Probl.", year="2011", pages="17 pages", volume="2011" } @Book{Coffey2004, author="W. T. Coffey, Y. P. Kalmykov, J. T. Waldron", title="The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering", year="2004", publisher="World Scientific Publishing Co.", address="River Edge" } @Article{Fazli2018, author="H. Fazli, J. J. Nieto", title="Fractional Langevin equation with anti-periodic boundary conditions", journal="Chaos Solitons Fractals", year="2018", pages="332--337", volume="114" } @Article{Gao2016, author="Z. Y. Gao, X. L. Yu, J. R. Wang", title="Nonlocal problems for Langevin-type differential equations with two fractional-order derivatives", journal="Bound. Value Probl.", year="2016", pages="21 pages", volume="2016" } @Book{Kilbas2006, author="A. A. Kilbas, H. M. Srivastava, J. J. Trujillo", title="Theory and applications of fractional differential equations", year="2006", publisher="Elsevier Science B.V.", address="Amsterdam" } @Article{Krasnoselskii1955, author="M. A. Krasnoselskii", title="Two remarks on the method of successive approximations", journal="Uspekhi Mat. Nauk (N.S.)", year="1955", pages="123--127", volume="10" } @Article{Li2014, author="X. Z. Li, M. Medved', J. R. Wang", title="Generalized Boundary Value Problems for Nonlinear Fractional Langevin Equations", journal="Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math.", year="2014", pages="85--100", volume="53" } @Article{Li2017, author="B. X. Li, S. R. Sun, Y. Sun", title="Existence of solutions for fractional Langevin equation with infinite-point boundary conditions", journal="J. Appl. Math. Comput.", year="2017", pages="683--692", volume="53" } @Article{Linz1999, author="S. J. Linz, J. C. Sprott", title="Elementary chaotic flow", journal="Phys. Lett. A", year="1999", pages="240--245", volume="259" } @Article{Mainradi1996, author="F. Mainradi, P. Pironi", title="The fractional Langevin equation: Brownian motion revisited", journal="Extracta Math.", year="1996", pages="140--154", volume="11" } @Article{Muensawat2017, author="T. Muensawat, S. K. Ntouyas, J. Tariboon", title="Systems of generalized Sturm-Liouville and Langevin fractional differential equations", journal="Adv. Difference Equ.", year="2017", pages="15 pages", volume="2017" } @Book{Podlubny1999, author="I. Podlubny", title="Fractional Differential Equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications", year="1999", publisher="Academic Press", address="San Diego" } @Article{Salem2019, author="A. Salem, F. Alzahrani, L. Almaghamsi", title="Fractional Langevin equation with nonlocal integral boundary condition", journal="Mathematics", year="2019", pages="1--10", volume="7" } @Article{Sprott2017, author="J. C. Sprott", title="Some simple chaotic jerk functions", journal="Amer. J. Phys.", year="2017", pages="537--543", volume="65" } @Article{Sprott2000, author="J. C. Sprott", title="A new class of chaotic circuit", journal="Phys. Lett. A", year="2000", pages="19--23", volume="266" } @Article{Sprott2011, author="J. C. Sprott", title="A new chaotic Jerk circuit", journal="IEEE Tran. Citcuit Syst. A", year="2011", pages="240--243", volume="58" } @Article{Sudsutad2013, author="W. Sudsutad, J. Tariboon", title="Nonlinear fractional integro-differential Langevin equation involving two fractional orders with three-point multi-term fractional integral boundary conditions", journal="J. Appl. Math. Comput.", year="2013", pages="507--522", volume="43" } @Article{Yu2014, author="T. Yu, K. Deng, M. Luo", title="Existence and uniqueness of solutions of initial value problems for nonlinear Langevin equation involving two fractional orders", journal="Commun. Nonlinear Sci. Numer. Simul.", year="2014", pages="1661--1668", volume="19" } @Article{Yukunthorn2014, author="W. Yukunthorn, S. K. Ntouyas, J. Tariboon", title="Nonlinear fractional Caputo-Langevin equation with nonlocal Riemann-Liouville fractional integral conditions", journal="Adv. Difference Equ.", year="2014", pages="18 pages", volume="2014" } @Article{Zhai2018, author="C. B. Zhai, P. P. Li", title="Nonnegative Solutions of Initial Value Problems for Langevin Equations Involving Two Fractional Orders", journal="Mediterr. J. Math.", year="2018", pages="11 pages", volume="15" } @Article{Zhai2018, author="C. B. Zhai, P. P. Li, H. Y. Li", title="Single upper-solution or lower-solution method for Langevin equations with two fractional orders", journal="Adv. Difference Equ.", year="2018", pages="10 pages", volume="2018" } @Article{Zhao2015, author="K. H. Zhao, P. Gong", title="Existence of positive solutions for a class of higher-order Caputo fractional differential equation", journal="Qual. Theory Dyn. Syst.", year="2015", pages="157--171", volume="14" } @Article{Zhou2018, author="Z. F. Zhou, Y. Qiao", title="Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions", journal="Bound. Value Probl.", year="2018", pages="10 pages", volume="2018" }