带p(t)-Laplacian算子的分数阶Langevin方程反周期边值问题解的存在性

Abstract

Abstract:

This paper studies the anti-periodic boundary value problems of fractional Langevin equation with p (t)-Laplacian operator. The sufficient conditions for the existence of solutions are obtained by using Schaefer fixed point theorem, and the main result is well illustrated with the aid of an example. The results obtained in this paper extend and enrich the existing related works.

Key words: Fractional differential equation, Anti-periodic boundary value problem, p (t)-Laplacian operator, Schaefer fixed point theorem

CLC Number:

O175.8

Jifeng Zhang,Wei Zhang,Jinbo Ni,Dandan Ren. Existence of Solutions for Anti-Periodic Boundary Value Problems of Fractional Langevin Equation with p(t)-Laplacian Operator[J].Acta mathematica scientia,Series A, 2021, 41(4): 1024-1032.

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References 28

1	林宗涵. 热力学与统计物理学. 北京: 北京大学出版社, 2007
	Lin Z H . Thermodynamics and Statistical Physics. Beijing: Peking University Press, 2007
2	陈文, 孙洪广, 李西成. 力学与工程问题的分数阶导数建模. 北京: 科学出版社, 2010
	Chen W , Sun H G , Li X C . Fractional Derivative Modeling of Mechanical and Engineering Problems. Beijing: Science Press, 2010
3	Lutz E . Fractional Langevin equation. Phys Rev E, 2001, 64 (5): 051106 doi: 10.1103/PhysRevE.64.051106
4	Burov S, Barkai E. The critical exponent of the fractional Langevin equation is a_c ≈ 0.402. 2007, arXiv: 0712.3407
5	刘玉记. 含三个Riemann-Liouville分数阶导数的脉冲Langevin型方程的边值问题的可解性. 数学物理学报, 2020, 40A (1): 103- 131 doi: 10.3969/j.issn.1003-3998.2020.01.009
	Liu Y J . Solvability of BVPs for impulsive fractional Langevin type equations involving three Riemann-Liouville fractional derivatives. Acta Math Sci, 2020, 40A (1): 103- 131 doi: 10.3969/j.issn.1003-3998.2020.01.009
6	蒲琳涓, 杨晓忠, 孙淑珍. 一类分数阶Langevin方程预估校正算法的数值分析. 数学物理学报, 2020, 40A (4): 1018- 1028 doi: 10.3969/j.issn.1003-3998.2020.04.017
	Pu L J , Yang X Z , Sun S Z . Numerical analysis of a class of fractional Langevin equation by predictor-corrector method. Acta Math Sci, 2020, 40A (4): 1018- 1028 doi: 10.3969/j.issn.1003-3998.2020.04.017
7	Ahmad B , Nieto J J , Alsaedi A , El-Shahed M . A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Anal Real World Appl, 2012, 13 (2): 599- 606 doi: 10.1016/j.nonrwa.2011.07.052
8	Zhou H , Alzabut J , Yang L . On fractional Langevin differential equations with anti-periodic boundary conditions. Eur Phys J Special Topics, 2017, 226 (16-18): 3577- 3590 doi: 10.1140/epjst/e2018-00082-0
9	Fazli H , Nieto J J . Fractional Langevin equation with anti-periodic boundary conditions. Chaos Solitons Fractals, 2018, 114, 332- 337 doi: 10.1016/j.chaos.2018.07.009
10	Wang G T , Qin J F , Zhang L H , Baleanu D . Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions. Chaos Solitons Fractals, 2020, 131, 109476 doi: 10.1016/j.chaos.2019.109476
11	Zhai C B , Li P P . Nonnegative solutions of initial value problems for Langevin equations involving two fractional orders. Mediterr J Math, 2018, 15, 164 doi: 10.1007/s00009-018-1213-x
12	Baghani O . On fractional Langevin equation involving two fractional orders. Commun Nonlinear Sci Numer Simul, 2017, 42, 675- 681 doi: 10.1016/j.cnsns.2016.05.023
13	Wang J R , Li X Z . Ulam-Hyers stability of fractional Langevin equations. Appl Math Comput, 2015, 258, 72- 83
14	Baghani H . An analytical improvement of a study of nonlinear Langevin equation involving two fractional orders in different intervals. J Fixed Point Theory Appl, 2019, 21 (4): 95 doi: 10.1007/s11784-019-0734-7
15	Zhou Z F , Qiao Y . Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions. Bound Value Probl, 2018, 2018, 152 doi: 10.1186/s13661-018-1070-3
16	Salem A , Alzahrani F , Alghamdi B . Langevin equation involving two fractional orders with three-point boundary conditions. Differential Integral Equations, 2020, 33 (3/4): 163- 180
17	Shen T F , Liu W B . Existence of solutions for fractional integral boundary value problems with p(t)-Laplacian operator. J Nonlinear Sci Appl, 2016, 9 (7): 5000- 5010
18	Xue T T , Liu W B , Shen T F . Existence of solutions for fractional Sturm-Liouville boundary value problems with p(t)-Laplacian operator. Bound Value Probl, 2017, 2017, 169 doi: 10.1186/s13661-017-0900-z
19	Shen X H , Shen T F . Existence of solutions for Erdélyi-Kober fractional integral boundary value problems with p(t)-Laplacian operator. Adv Difference Equa, 2020, 2020, 565 doi: 10.1186/s13662-020-03015-y
20	Tang X S , Wang X C , Wang Z W , Ouyang P C . The existence of solutions for mixed fractional resonant boundary value problem with p(t)-Laplacian operator. J Appl Math Comput, 2019, 61 (1/2): 559- 572 doi: 10.1007/s12190-019-01264-z
21	Tang X S , Luo J Y , Zhou S , Yan C Y . Existence of positive solutions of mixed fractional integral boundary value problem with p(t)-Laplacian operator. Ric Mat, 2020, doi: 10.1007/s11587-020-00542-4
22	Wang G T , Ren X Y , Zhang L H , Ahmad B . Explicit iteration and unique positive solution for a Caputo-Hadamard fractional turbulent flow model. IEEE Access, 2019, 7, 109833- 109839 doi: 10.1109/ACCESS.2019.2933865
23	Chen Y M , Levine S , Rao M . Variable exponent, linear growth functionals in image restoration. SIAM J Appl Math, 2006, 66 (4): 1383- 1406 doi: 10.1137/050624522
24	Růžička M . Electrorheological Fluids: Modeling and Mathematical Theory. Berlin: Springer-Verlag, 2000
25	Zhikov V V . Averaging of functionals of the calculus of variations and elasticity theory. Izv Akad Nauk SSSR Ser Mat, 1986, 50 (4): 675- 710
26	Zhang Q H . Existence of solutions for weighted p(r)-Laplacian system boundary value problems. J Math Anal Appl, 2007, 327 (1): 127- 141 doi: 10.1016/j.jmaa.2006.03.087
27	Kilbas A A , Srivastava H M , Trujillo J J . Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006,
28	Zhou Y , Wang J R , Zhang L . Basic Theory of Fractional Differential Equations. Second edition. Singapore: World Scientific, 2017

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Existence of Solutions for Anti-Periodic Boundary Value Problems of Fractional Langevin Equation with p(t)-Laplacian Operator

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