Existence of Positive Solutions to Two-Point Boundary Value Problems of Fractional Differentional Equations Involving Caputo-Fabrizio Fractional Derivatives

doi:10.13438/j.cnki.jdzk.2023.05.001

Abstract

Abstract: Based on the Krasnoselskii fixed point theorem，existence of positive solutions to two-point boundary value problems for fractional differential equations involving the Caputo-Fabrizio derivative is discussed，and some sufficient conditions are established to ensure the existence of at least one positive solutions to the boundary problem.

Key words: fractional differential equations, Caputo-Fabrizio derivatives, boundary value problems, positive solutions, fixed points

WANG Lanfang. Existence of Positive Solutions to Two-Point Boundary Value Problems of Fractional Differentional Equations Involving Caputo-Fabrizio Fractional Derivatives[J]. Journal of Jishou University(Natural Sciences Edition), 2023, 44(5): 1-5.

References

[1] KILBAS A A A,SRIVASTAVA HARI MOHAN,TRUJILLO JUAN J.Theory and Applications of Fractional Differential Equations[M]∥North-Hollan Mathematics Studies.Amsterdam:Elsevier Science B.V.,2006.
[2] STANISLAVSKY A,WERON K.Two-Time Scale Subordination in Physical Processes with Long-Term Memory[J].Annals of Physics,2008,323(3):643-653.
[3] HARKO TIBERIU,LEUNG CHUN SING,MOCANU GABRIELA.Generalized Langevin Equation with Colored Noise Description of the Stochastic Oscillations of Accretion Disks[J].European Physical Journal C,2014,74:2900.
[4] CAPUTO MICHELE,FABRIZIO MAURO.A New Definition of Fractional Derivative Without Singular Kernel[J].Progress in Fractional Differentiation and Applications,2015,2:73-75.
[5] ATANGANA ABDON,BALEANU DUMITRU.New Fractional Derivatives with Nonlocal and Non-Singular Kernel:Theory and Application to Heat Transfer Model[J].Thermal Science,2016,20(2):763-769.
[6] NISAR KOTTAKKARAN SOOPPY,FARMAN MUHAMMAD,HINCAL EVREN,et al.Modelling and Analysis of Bad Impact of Smoking in Society with Constant Proportional-Caputo Fabrizio Operator[J].Chaos,Soliton & Fractals,2023,172:113549.DOI:10.1016/j.chaos.2023.113549.
[7] NGUYEN H T,NGUYEN A T,NGUYEN HUU H C.Existence and Continuity Results for Kirchhoff Parabolic Equation with Caputo-Fabrizio Operator[J].Chaos,Soliton & Fractals,2023,167:113028.DOI:10.1016/j.chaos.2022.113028.
[8] ZHONG Wenyong,WANG Lanfang,ABDELJAWAD THABET.Separation and Stability of Solutions to Nonlinear Systems Involving Caputo-Fabrizio Derivatives[J].Advances in Difference Equations,2020,2020:166.
[9] RAVICHANDRAN C,LOGESWARI K,GMEZ-AGUILAR J F.An Epidemiological Model for Computer Virus with Atangana-Baleanu Fractional Derivative[J].Results in Physics,2023,8:1-8.
[10] ABDELJAWAD THABET.Fractional Operators with Exponential Kernels and a Lyapunov Type Inequality[J].Advances in Difference Equations,2017,2017:313.
[11] ABDELJAWAD THABET.A Lyapunov Type Inequality for Fractional Operators with Nonsingular Mittag-Leffler Kernel[J].Journal of Inequalities and Applications,2017(1):130.
[12] KRASNOSEL' SKII M A.Positive Solutions of Operator Equations[M].Groningen:P.Noordhof Ltd.,1964:135-137.

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[2]	LI Yiyun, XIE Jingli. Existence and Uniqueness of Solutions for a Class of Fractional Differential Equations with Boundary Value Problems [J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 1-6.
[3]	DUAN Lijing, XIE Jingli, LIU Hanyan. Existence of Solutions for Boundary Value Problems of Hilfer-Hadamard Type Fractional Differential Equations [J]. Journal of Jishou University(Natural Sciences Edition), 2021, 42(3): 6-12.
[4]	ZHANG Yuyao, ZHONG Wenyong. Global Existence and Stability of Solutions of Tempered Fractional Differential Equations [J]. Journal of Jishou University（Natural Sciences Edition), 2020, 41(2): 5-8.
[5]	SHI Min. Existence of Positive Solutions of Nonlinear Fractional Differential Equations [J]. Journal of Jishou University（Natural Sciences Edition), 2018, 39(5): 8-13.
[6]	OUYANG Min , ZHONG Wen-Yong. Investigation on Multipoint Boundary Value Problems of Fractional Differential Equations with Parameters [J]. journal6, 2015, 36(2): 16-19.
[7]	XU Shao-Yuan. On Random Fixed Point Theorems of Random Condensing Operators and Applications [J]. journal6, 2015, 36(2): 8-10.
[8]	WANG Lan-Fang. Nonlinear Boundary Value Problems of Fractional Differential Equations [J]. journal6, 2014, 35(6): 7-9.
[9]	CAO Yin-Fang, XIAO Jian-Zhong, SHEN Zhi-Mo. Existence of Triple Positive Solutions for Three-Point Boundary Value Problems of Fourth-Order Differential Equations [J]. journal6, 2011, 32(5): 26-31.
[10]	LIU Qian, SUN Qin-Fu, OuYang-Jin-Gang . Existence of Positive Solutions to Singular Fourth-Order Boundary Value Problems with Two Parameters [J]. journal6, 2010, 31(3): 15-20.
[11]	ZHONG Wen-Yong. Positive Solutions to Nonhomogeneous Boundary Value Problem for Fractional Differential Equations [J]. journal6, 2010, 31(3): 10-14.
[12]	ZHONG Wen-Yong. Positive Solutions for Multiple-Point Boundary Value Problem of Fractional Differential Equations [J]. journal6, 2010, 31(1): 9-12.
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[15]	NI Ren-Xing. Necessary and Sufficient Conditions for Strongly　Convergence of Iterative Sequence of Asymptotically Pseudo-Contraction Mapping [J]. journal6, 2004, 25(3): 1-5.