TY - CHAP AU - Kilbas, A. A. AU - Srivastava, H. M. AU - Trujillo, J. J. PY - 2006 DA - 2006// TI - North-Holland Mathematics Studies 204 BT - Theory and Applications of Fractional Differential Equations PB - Elsevier CY - Amsterdam ID - Kilbas2006 ER - TY - CHAP AU - Podlubny, I. PY - 1999 DA - 1999// TI - Mathematics in Science and Engineering BT - Fractional Differential Equations PB - Academic Press CY - New York ID - Podlubny1999 ER - TY - BOOK PY - 2007 DA - 2007// TI - Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering PB - Springer CY - Dordrecht ID - ref3 ER - TY - JOUR AU - Ahmad, B. AU - Nieto, J. J. PY - 2012 DA - 2012// TI - Sequential fractional differential equations with three-point boundary conditions JO - Comput. Math. Appl VL - 64 UR - https://doi.org/10.1016/j.camwa.2012.02.036 DO - 10.1016/j.camwa.2012.02.036 ID - Ahmad2012 ER - TY - JOUR AU - Kaslik, E. AU - Sivasundaram, S. PY - 2012 DA - 2012// TI - Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions JO - Nonlinear Anal., Real World Appl VL - 13 UR - https://doi.org/10.1016/j.nonrwa.2011.11.013 DO - 10.1016/j.nonrwa.2011.11.013 ID - Kaslik2012 ER - TY - JOUR AU - Guezane-Lakoud, A. AU - Khaldi, R. PY - 2012 DA - 2012// TI - Solvability of a fractional boundary value problem with fractional integral condition JO - Nonlinear Anal VL - 75 UR - https://doi.org/10.1016/j.na.2011.11.014 DO - 10.1016/j.na.2011.11.014 ID - Guezane-Lakoud2012 ER - TY - JOUR AU - Zhou, P. AU - Zhu, W. PY - 2011 DA - 2011// TI - Function projective synchronization for fractional-order chaotic systems JO - Nonlinear Anal., Real World Appl VL - 12 UR - https://doi.org/10.1016/j.nonrwa.2010.08.008 DO - 10.1016/j.nonrwa.2010.08.008 ID - Zhou2011 ER - TY - JOUR AU - Goodrich, C. S. PY - 2011 DA - 2011// TI - Existence of a positive solution to systems of differential equations of fractional order JO - Comput. Math. Appl VL - 62 UR - https://doi.org/10.1016/j.camwa.2011.02.039 DO - 10.1016/j.camwa.2011.02.039 ID - Goodrich2011 ER - TY - JOUR AU - Agarwal, R. P. AU - Benchohra, M. AU - Hamani, S. AU - Pinelas, S. PY - 2011 DA - 2011// TI - Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half-line JO - Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal VL - 18 ID - Agarwal2011 ER - TY - CHAP AU - Baleanu, D. AU - Agarwal, R. P. AU - Mustafa, O. G. AU - Cosulschi, M. PY - 2011 DA - 2011// TI - Asymptotic integration of some nonlinear differential equations with fractional time derivative BT - J. Phys. A ID - Baleanu2011 ER - TY - JOUR AU - Agarwal, R. P. AU - Zhou, Y. AU - Wang, J. AU - Luo, X. PY - 2011 DA - 2011// TI - Fractional functional differential equations with causal operators in Banach spaces JO - Math. Comput. Model VL - 54 UR - https://doi.org/10.1016/j.mcm.2011.04.016 DO - 10.1016/j.mcm.2011.04.016 ID - Agarwal2011 ER - TY - JOUR AU - Wang, G. AU - Agarwal, R. P. AU - Cabada, A. PY - 2012 DA - 2012// TI - Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations JO - Appl. Math. Lett VL - 25 UR - https://doi.org/10.1016/j.aml.2011.09.078 DO - 10.1016/j.aml.2011.09.078 ID - Wang2012 ER - TY - JOUR AU - Chen, F. AU - Nieto, J. J. AU - Zhou, Y. PY - 2012 DA - 2012// TI - Global attractivity for nonlinear fractional differential equations JO - Nonlinear Anal., Real World Appl VL - 13 UR - https://doi.org/10.1016/j.nonrwa.2011.07.034 DO - 10.1016/j.nonrwa.2011.07.034 ID - Chen2012 ER - TY - JOUR AU - Wang, J. AU - Zhou, Y. PY - 2011 DA - 2011// TI - A class of fractional evolution equations and optimal controls JO - Nonlinear Anal VL - 12 UR - https://doi.org/10.1016/j.nonrwa.2010.06.013 DO - 10.1016/j.nonrwa.2010.06.013 ID - Wang2011 ER - TY - CHAP AU - Wang, G. AU - Ntouyas, S. K. AU - Zhang, L. PY - 2011 DA - 2011// TI - Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument BT - Adv. Differ. Equ ID - Wang2011 ER - TY - BOOK PY - 1954 DA - 1954// TI - Selected Papers on Noise and Stochastic Processes PB - Dover CY - New York ID - ref16 ER - TY - BOOK AU - Mazo, R. PY - 2002 DA - 2002// TI - Brownian Motion: Fluctuations, Dynamics and Applications PB - Oxford Univ. Press CY - Oxford ID - Mazo2002 ER - TY - BOOK AU - Coffey, W. T. AU - Kalmykov, Y. P. AU - Waldron, J. T. PY - 2004 DA - 2004// TI - The Langevin Equation PB - World Scientific CY - Singapore ID - Coffey2004 ER - TY - JOUR AU - Kobolev, V. AU - Romanov, E. PY - 2000 DA - 2000// TI - Fractional Langevin equation to describe anomalous diffusion JO - Prog. Theor. Phys. Suppl VL - 139 UR - https://doi.org/10.1143/PTPS.139.470 DO - 10.1143/PTPS.139.470 ID - Kobolev2000 ER - TY - CHAP AU - Lim, S. C. AU - Muniandy, S. V. PY - 2002 DA - 2002// TI - Self-similar Gaussian processes for modeling anomalous diffusion BT - Phys. Rev. E ID - Lim2002 ER - TY - CHAP AU - Picozzi, S. AU - West, B. PY - 2002 DA - 2002// TI - Fractional Langevin model of memory in financial markets BT - Phys. Rev. E ID - Picozzi2002 ER - TY - JOUR AU - Lim, S. C. AU - Li, M. AU - Teo, L. P. PY - 2007 DA - 2007// TI - Locally self-similar fractional oscillator processes JO - Fluct. Noise Lett VL - 7 UR - https://doi.org/10.1142/S0219477507003817 DO - 10.1142/S0219477507003817 ID - Lim2007 ER - TY - JOUR AU - Lim, S. C. AU - Li, M. AU - Teo, L. P. PY - 2008 DA - 2008// TI - Langevin equation with two fractional orders JO - Phys. Lett. A VL - 372 UR - https://doi.org/10.1016/j.physleta.2008.08.045 DO - 10.1016/j.physleta.2008.08.045 ID - Lim2008 ER - TY - BOOK AU - Lim, S. C. AU - Teo, L. P. PY - 2009 DA - 2009// TI - The fractional oscillator process with two indices ID - Lim2009 ER - TY - CHAP AU - Ahmad, B. AU - Nieto, J. J. PY - 2010 DA - 2010// TI - Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions BT - Int. J. Differ. Equ ID - Ahmad2010 ER - TY - JOUR AU - Ahmad, B. AU - Nieto, J. J. AU - Alsaedi, A. AU - El-Shahed, M. PY - 2012 DA - 2012// TI - A study of nonlinear Langevin equation involving two fractional orders in different intervals JO - Nonlinear Anal., Real World Appl VL - 13 UR - https://doi.org/10.1016/j.nonrwa.2011.07.052 DO - 10.1016/j.nonrwa.2011.07.052 ID - Ahmad2012 ER - TY - JOUR AU - Byszewski, L. AU - Lakshmikantham, V. PY - 1991 DA - 1991// TI - Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space JO - Appl. Anal VL - 40 UR - https://doi.org/10.1080/00036819008839989 DO - 10.1080/00036819008839989 ID - Byszewski1991 ER - TY - JOUR AU - Byszewski, L. PY - 1991 DA - 1991// TI - Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem JO - J. Math. Anal. Appl VL - 162 UR - https://doi.org/10.1016/0022-247X(91)90164-U DO - 10.1016/0022-247X(91)90164-U ID - Byszewski1991 ER - TY - JOUR AU - Balachandran, K. AU - Trujillo, J. J. PY - 2010 DA - 2010// TI - The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces JO - Nonlinear Anal VL - 72 UR - https://doi.org/10.1016/j.na.2010.02.035 DO - 10.1016/j.na.2010.02.035 ID - Balachandran2010 ER - TY - JOUR AU - N’Guerekata, G. M. PY - 2009 DA - 2009// TI - A Cauchy problem for some fractional abstract differential equation with nonlocal condition JO - Nonlinear Anal VL - 70 UR - https://doi.org/10.1016/j.na.2008.02.087 DO - 10.1016/j.na.2008.02.087 ID - N’Guerekata2009 ER - TY - CHAP AU - Feng, M. AU - Zhang, X. AU - Ge, W. PY - 2011 DA - 2011// TI - New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions BT - Bound. Value Probl ID - Feng2011 ER - TY - JOUR AU - Salem, H. A. H. PY - 2011 DA - 2011// TI - Fractional order boundary value problem with integral boundary conditions involving Pettis integral JO - Acta Math. Sci VL - 31 UR - https://doi.org/10.1016/S0252-9602(11)60266-X DO - 10.1016/S0252-9602(11)60266-X ID - Salem2011 ER - TY - JOUR AU - Ahmad, B. AU - Nieto, J. J. AU - Alsaedi, A. PY - 2011 DA - 2011// TI - Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions JO - Acta Math. Sci VL - 31 UR - https://doi.org/10.1016/S0252-9602(11)60388-3 DO - 10.1016/S0252-9602(11)60388-3 ID - Ahmad2011 ER - TY - CHAP AU - Ahmad, B. AU - Nieto, J. J. PY - 2009 DA - 2009// TI - Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions BT - Bound. Value Probl ID - Ahmad2009 ER - TY - CHAP AU - Ahmad, B. AU - Ntouyas, S. K. AU - Alsaedi, A. PY - 2011 DA - 2011// TI - New existence results for nonlinear fractional differential equations with three-point integral boundary conditions BT - Adv. Differ. Equ ID - Ahmad2011 ER - TY - JOUR AU - Benchohra, M. AU - Graef, J. R. AU - Hamani, S. PY - 2008 DA - 2008// TI - Existence results for boundary value problems with nonlinear fractional differential equations JO - Appl. Anal VL - 87 UR - https://doi.org/10.1080/00036810802307579 DO - 10.1080/00036810802307579 ID - Benchohra2008 ER - TY - JOUR AU - Hamani, S. AU - Benchohra, M. AU - Graef, J. R. PY - 2010 DA - 2010// TI - Existence results for boundary value problems with nonlinear fractional inclusions and integral conditions JO - Electron. J. Differ. Equ VL - 20 UR - https://doi.org/10.14232/ejqtde.2010.1.32 DO - 10.14232/ejqtde.2010.1.32 ID - Hamani2010 ER - TY - JOUR AU - Liu, X. AU - Jia, M. AU - Wu, B. PY - 2009 DA - 2009// TI - Existence and uniqueness of solution for fractional differential equations with integral boundary conditions JO - Electron. J. Qual. Theory Differ. Equ VL - 69 ID - Liu2009 ER - TY - JOUR AU - Cabada, A. AU - Wang, G. PY - 2012 DA - 2012// TI - Positive solutions of nonlinear fractional differential equations with integral boundary value conditions JO - J. Math. Anal. Appl VL - 389 UR - https://doi.org/10.1016/j.jmaa.2011.11.065 DO - 10.1016/j.jmaa.2011.11.065 ID - Cabada2012 ER - TY - JOUR AU - Benchohra, M. AU - Hamani, S. AU - Ntouyas, S. K. PY - 2009 DA - 2009// TI - Boundary value problems for differential equations with fractional order and nonlocal conditions JO - Nonlinear Anal VL - 71 UR - https://doi.org/10.1016/j.na.2009.01.073 DO - 10.1016/j.na.2009.01.073 ID - Benchohra2009 ER - TY - STD TI - Wang, G, Ahmad, B, Zhang, L: New existence results for nonlinear impulsive integro-differential equations of fractional order with nonlocal boundary conditions. Nonlinear Stud. (to appear) ID - ref41 ER - TY - JOUR AU - Wang, G. AU - Ahmad, B. AU - Zhang, L. PY - 2011 DA - 2011// TI - Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions JO - Comput. Math. Appl VL - 62 UR - https://doi.org/10.1016/j.camwa.2011.04.004 DO - 10.1016/j.camwa.2011.04.004 ID - Wang2011 ER - TY - JOUR AU - Wang, G. AU - Ahmad, B. AU - Zhang, L. PY - 2011 DA - 2011// TI - Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order JO - Nonlinear Anal VL - 74 UR - https://doi.org/10.1016/j.na.2010.09.030 DO - 10.1016/j.na.2010.09.030 ID - Wang2011 ER - TY - CHAP AU - Zhang, L. AU - Wang, G. PY - 2011 DA - 2011// TI - Existence of solutions for nonlinear fractional differential equations with impulses and anti-periodic boundary conditions BT - Electron. J. Qual. Theory Differ. Equ ID - Zhang2011 ER - TY - JOUR AU - Ahmad, B. AU - Wang, G. PY - 2011 DA - 2011// TI - A study of an impulsive four-point nonlocal boundary value problem of nonlinear fractional differential equations JO - Comput. Math. Appl VL - 62 UR - https://doi.org/10.1016/j.camwa.2011.04.033 DO - 10.1016/j.camwa.2011.04.033 ID - Ahmad2011 ER - TY - JOUR AU - Ahmad, B. AU - Nieto, J. J. PY - 2011 DA - 2011// TI - Existence of solutions for impulsive anti-periodic boundary value problems of fractional order JO - Taiwan. J. Math VL - 15 ID - Ahmad2011 ER - TY - JOUR AU - Ahmad, B. AU - Sivasundaram, S. PY - 2010 DA - 2010// TI - Existence of solutions for impulsive integral boundary value problems of fractional order JO - Nonlinear Anal. Hybrid Syst VL - 4 UR - https://doi.org/10.1016/j.nahs.2009.09.002 DO - 10.1016/j.nahs.2009.09.002 ID - Ahmad2010 ER - TY - JOUR AU - Agarwal, R. P. AU - Ahmad, B. PY - 2011 DA - 2011// TI - Existence of solutions for impulsive anti-periodic boundary value problems of fractional semilinear evolution equations JO - Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal VL - 18 ID - Agarwal2011 ER - TY - JOUR AU - Mophou, G. M. PY - 2010 DA - 2010// TI - Existence and uniqueness of mild solutions to impulsive fractional differential equations JO - Nonlinear Anal VL - 72 UR - https://doi.org/10.1016/j.na.2009.08.046 DO - 10.1016/j.na.2009.08.046 ID - Mophou2010 ER - TY - JOUR AU - Tian, Y. AU - Bai, Z. PY - 2010 DA - 2010// TI - Existence results for the three-point impulsive boundary value problem involving fractional differential equations JO - Comput. Math. Appl VL - 59 UR - https://doi.org/10.1016/j.camwa.2010.01.028 DO - 10.1016/j.camwa.2010.01.028 ID - Tian2010 ER - TY - JOUR AU - Zhang, X. AU - Huang, X. AU - Liu, Z. PY - 2010 DA - 2010// TI - The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay JO - Nonlinear Anal. Hybrid Syst VL - 4 UR - https://doi.org/10.1016/j.nahs.2010.05.007 DO - 10.1016/j.nahs.2010.05.007 ID - Zhang2010 ER -