NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(13)60044-2

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 847-854.doi: 10.1016/S0252-9602(13)60044-2

NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

李楠|王长有

Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China； College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

收稿日期:2012-02-06 出版日期:2013-05-20 发布日期:2013-05-20
基金资助:
This work is supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of China, Natural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of China, and National Natural Science Foundation of China (11101298).

NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

LI Nan, WANG Chang-You

Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China； College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2012-02-06 Online:2013-05-20 Published:2013-05-20
Supported by:
This work is supported by Science and Technology Project of Chongqing Municipal Education Committee (kJ110501) of China, Natural Science Foundation Project of CQ CSTC (cstc2012jjA20016) of China, and National Natural Science Foundation of China (11101298).

摘要/Abstract

摘要：

In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results.

关键词: Fractional differential equations, positive solution, upper and lower solutions, existence and uniqueness, fixed point theorem

Abstract:

Key words: Fractional differential equations, positive solution, upper and lower solutions, existence and uniqueness, fixed point theorem

中图分类号:

34B15

李楠, 王长有. NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(3): 847-854.

LI Nan, WANG Chang-You. NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2013, 33(3): 847-854.

参考文献

[1] Mainardi F. The fundamental solutions for the fractional diffusion-wave equation. Appl Math Letters, 1996, 9: 23–28

[2] Buckwar E, Luchko Y. Invariance of a partial differential equation of fractional order under lie group of scaling trabsformations. J Math Anal Appll, 1998, 227: 81–97

[3] Zhu Z, Li G, Cheng C. Quasi-static and dynamical analysis for viscoelastic timoshenko beam with fractional derivative constitutive relation. Appl Math Mech, 2002, 23: 1–15

[4] Delbosco D, Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J Math Anal Appl, 1996, 204: 609–625

[5] Zhang S. The existence of a positive solution for a fractional differential equation. J Math Anal Appl, 2000, 252: 804–812

[6] Yao Q. Existence of positive solution for a class of sublinear fractional differential equations. Acta Mathe-maticae Applicatae Sinica, 2005, 28: 429–434 (Chinese)

[7] Ladshmikantham V, Vatsals A S. Basic theory of fractional differential equations. Nonlinear Anal: TMA, 2008, 60: 2677–2682

[8] Wang C. Existence and stability of periodic solutions for parabolic systems with time delays.J Math Anal Appl, 2008, 339: 1354-1361

[9] Belmekki M, Nieto J J, Rodriguez-Lopez R. Existence of periodic solutions for a nonlinear fractional differential equation. Boundary Value Problems, 2009, 2009: Art ID 324561

[10] Chang Y K, Nieto J J. Some new existence results for fractional differential inclusions with boundary conditions. Math Comput Modelling, 2009, 49: 605–609

[11] Bonilla B, Rivero M, Rodriguez-Germa L, Trujillo J J. Fractional differential equations as al ternative models to nonlinear differential equations. Appl Math Comput, 2007, 187: 79–88

[12] Kosmatov N. Integral equations and initial value problems for nonlinear differential equations of fractional order. Nonlinear Anal: TMA, 2009, 70: 2521–2529

[13] Bai Z B, Qiu T T. Existence of positive solution for singular fractional differential equation. Appl Math Comput, 2009, 215: 2761–2767

[14] Jumarie G. An approach via fractional analysis to non-linearity induced by coarse-graining in space. Non-linear Analysis: RWA , 2010, 11: 535–546

[15] Agarwal R P, Lakshmikantham V, NietoJ J. On the concept of solution for fractional differe ntial equations with uncertainty. Nonlinear Anal: TMA, 2010, 72: 2859–2862

[16] Wei Z, Che J. Initial value problems for fractional differential equations involving Riemann- Liouville sequential fractional derivative. J Math Anal Appl, 2010, 367: 260-272

[17] Krishnan B, Trujillo J J. The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces. Nonlinear Anal: TMA, 2010, 72: 4587–4593

[18] Jiang W. The constant variation formulae for singular fractional differential systems with delay. Computers and Mathematics with Applications, 2010, 59: 1184–1190

[19] Wang C, Wang R, Wang S, Yang C. Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation. Boundary Value Problems, 2011, 2011: Art ID 297026

[20] Wang J, Zhou Y. Analysis of nonlinear fractional control systems in Banach spaces. Nonlinear Anal: TMA, 2011, 74: 5929–5942

[21] Yang X, Wei Z, Dong W. Existence of positive solutions for the boundary value problem of nonlinear fractional differential equations. Commun Nonlinear Sci Numer Simulat, 2012, 17: 85–92

[22] Wang C, Wang S, Li L. Periodic solution and almost periodic solution of a nonmonotone reaction-diffusion system with time delay. Acta Mathematica Scientia, 2010, 30A(2): 517–524

[23] Wang Y, Liu L. Positive solutions for fractional m-point boundary value problem in Banach spaces. Acta Mathematica Scientia, 2012, 32A(1): 246–256

[24] Wang C, Zhang H, Wang S. Positive solution of a nonlinear fractional differential equation involving caputo derivative. Discrete Dynamics in Natural and Society, 2012, 2012: Art ID425408

[25] Zhang H, Zheng Z, Jiang W. Existence of solutions for nonlinear fractional order functional differential equations. Acta Mathematica Scientia, 2011, 31A(2): 289–297

NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	张肖, 吉国兴. SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA[J]. 数学物理学报(英文版), 2018, 38(4): 1143-1150.
[2]	王朋燕, 王永忠. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM[J]. 数学物理学报(英文版), 2018, 38(3): 935-949.
[3]	Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 377-390.
[4]	廖家锋, 蒲洋, 唐春雷. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH[J]. 数学物理学报(英文版), 2018, 38(2): 497-518.
[5]	贾慧芳, 李工宝. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2018, 38(2): 391-418.
[6]	宋威, 李林. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION[J]. 数学物理学报(英文版), 2018, 38(1): 177-186.
[7]	Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. 数学物理学报(英文版), 2017, 37(6): 1727-1739.
[8]	马如云, 高红亮. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN[J]. 数学物理学报(英文版), 2017, 37(5): 1472-1482.
[9]	Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON. A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(6): 1631-1640.
[10]	刘玉记. PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS[J]. 数学物理学报(英文版), 2016, 36(5): 1492-1508.
[11]	Yan LI. NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SEMI-LINEAR EQUATION INVOLVING THE FRACTIONAL LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2016, 36(3): 666-682.
[12]	Adnène ARBI, Farouk CHÉRIF, Chaouki AOUITI, Abderrahmen TOUATI. DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS[J]. 数学物理学报(英文版), 2016, 36(3): 891-912.
[13]	Dhananjay GOPAL, Mujahid ABBAS, Deepesh Kumar PATEL, Calogero VETRO. FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J]. 数学物理学报(英文版), 2016, 36(3): 957-970.
[14]	Anna BAHYRYCZ, Magdalena PISZCZEK. ON APPROXIMATELY (p, q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES[J]. 数学物理学报(英文版), 2016, 36(2): 593-601.
[15]	Sahbi BOUSSANDEL. EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES[J]. 数学物理学报(英文版), 2016, 36(1): 233-243.