[1] |
CoffeyWT, KalmykovYP, WaldronJT. The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering. Singapore:World Scientific; 2004. · Zbl 1098.82001 |
[2] |
AhmadB, NietoJJ, AlsaediA, El‐ShahedM. A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Anal Real World Appl. 2012;13:599‐606. · Zbl 1238.34008 |
[3] |
BaghaniO. On fractional Langevin equation involving two fractional orders. Commun Nonlinear Sci Numer Simulat. 2017;42:675‐681. · Zbl 1473.82025 |
[4] |
BerhailA, TaboucheN, MatarMM, AlzabutJ. Boundary value problem defined by system of generalized Sturm‐Liouville and Langevin Hadamard fractional differential equations. Math Method Appl Sci. https://doi.org/10.1002/mma.6507 · Zbl 07924814 · doi:10.1002/mma.6507 |
[5] |
BaghaniH. Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders. J Fixed Point Theory Appl. 2018;20:63. · Zbl 1397.34017 |
[6] |
BaleanuD, AlzabutJ, JonnalagaddaJM, AdjabiY, MatarMM. A coupled system of generalized Sturm‐Liouville problems and Langevin fractional differential equations in the frame of nonlocal and non‐singular derivatives. Adv Differ Equ. 2020;239(2020). https://doi.org/10.1186/s13662‐020‐02690‐1 · Zbl 1482.34015 · doi:10.1186/s13662‐020‐02690‐1 |
[7] |
BaghaniH, NietoJJ. On fractional Langevin equation involving two fractional orders in different intervals. Nonlinear Anal Model Control. 2019;24:884‐897. · Zbl 1439.34009 |
[8] |
LiB, SunS, SunY. Existence of solutions for fractional Langevin equation with infinite‐point boundary conditions. J Appl Math Comput. 2017;53:683‐692. · Zbl 1360.34015 |
[9] |
BerhailA, TaboucheN, MatarMM, AlzabutJ. On nonlocal integral and derivative boundary value problem of nonlinear Hadamard Langevin equation with three different fractional orders. Bol Soc Mat Mex. 2020;26:303‐318. https://doi.org/10.1007/s40590‐019‐00257‐z · Zbl 1446.34010 · doi:10.1007/s40590‐019‐00257‐z |
[10] |
YuT, DengK, LuoM. Existence and uniqueness of solutions of initial value problems for nonlinear Langevin equation involving two fractional orders. Commun Nonlinear Sci Numer Simulat. 2014;19:1661‐1668. · Zbl 1457.34020 |
[11] |
ZhouH, AlzabutJ, YangL. On fractional Langevin differential equations with anti‐periodic boundary conditions. European Phys J Special Top. 2017;226(16‐18):3577‐3590. |
[12] |
HendersonJ, LucaR, TudoracheA. On a system of fractional differential equations with coupled integral boundary conditions. Fract. Calc. Appl. Anal.2015;18:361‐386. · Zbl 1315.34012 |
[13] |
AgarwalRP, AhmadB, GaroutD, AlsaediA. Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi‐point boundary conditions. Chaos Solit Fract. 2017;102:149‐161. · Zbl 1374.34060 |
[14] |
AljoudiS, AhmadB, NietoJJ, AlsaediA. A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions. Chaos Solit Fract. 2016;91:39‐46. · Zbl 1372.34006 |
[15] |
SeemabA, RehmanM, AlzabutJ, HamdiA. On the existence of positive solutions for generalized fractional boundary value problems. Bound Value Prob. 2019;2019:186. https://doi.org/10.1186/s13661‐019‐01300‐8 · Zbl 1513.34116 · doi:10.1186/s13661‐019‐01300‐8 |
[16] |
WangJR, ZhangY. Analysis of fractional order differential coupled systems. Math Methods Appl Sci. 2015;38:3322‐3338. · Zbl 1336.34020 |
[17] |
AgarwalRP, BenchohraM, HamaniS. A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl Math. 2010;109:973‐1033. · Zbl 1198.26004 |
[18] |
SunJ, LiuY, LiuG. Existence of solutions for fractional differential systems with antiperiodic boundary conditions. Comput Math Appl. 2012;64:1557‐1566. · Zbl 1268.34157 |
[19] |
ZhouWX, ChuYD. Existence of solutions for fractional differential equations with multi‐point boundary conditions. Commun Nonlinear Sci Numer Simulat. 2012;17:1142‐1148. · Zbl 1245.35153 |
[20] |
AbbasS. Existence of solutions to fractional order ordinary and delay differential equations and applications. Elect J Diff Eq. 2011;2011(09):1‐11. · Zbl 1211.34096 |
[21] |
AbbasaS, ErturkVS, MomaniS. Dynamical analysis of the Irving Mullineux oscillator equation of fractional order. Signal Proc. 2014;102:171‐176. |
[22] |
AbbasS, BanerjeeM, MomaniS. Dynamical analysis of fractional‐order modified logistic model. Comput Math Appl. 2011;62(3):1098‐1104. · Zbl 1228.34008 |
[23] |
AhmadB, Otero‐EspinarV. Existence of solutions for fractional differential inclusions with anti‐periodic boundary conditions. Bound Value Probl. 2009:625347. · Zbl 1172.34004 |
[24] |
AhmadB, NietoJJ. Existence of solutions for anti‐periodic boundary value problems involving fractional differential equations via Leray Schauder degree theory. Topol Methods Nonlinear Anal. 2010;35:295‐304. · Zbl 1245.34008 |
[25] |
AhmadB. Existence of solutions for fractional differential equations of order with anti‐periodic boundary conditions. J Appl Math Comput. 2010;34:385‐391. · Zbl 1216.34003 |
[26] |
WangG, AhmadB, ZhangL. Impulsive anti‐periodic boundary value problem for nonlinear differential equations of fractional order. Nonlinear Anal Theory Methods Appl. 2011;74(3):792‐804. · Zbl 1214.34009 |
[27] |
SudsutadW, NtouyasSK, TariboonJ. Systems of fractional Langevin equations of Riemann‐Liouville and Hadamard types. Adv Diff Eq. 2015;2015:235. · Zbl 1422.34063 |
[28] |
FazliH, NietoJJ. Fractional Langevin equation with anti‐periodic boundary conditions. Chaos Solit Fract. 2018;114:332‐337. · Zbl 1415.34016 |
[29] |
KilbasAA, SrivastavaHM, TrujilloJJ. Theory and Applications of Fractional Differential Equations. Amsterdam:Elsevier; 2006. · Zbl 1092.45003 |
[30] |
PodlubnyI. Fractional Differential Equations. New York:Academic Press; 1999. · Zbl 0924.34008 |