FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

doi:10.1016/S0252-9602(11)60266-X

摘要/Abstract

摘要：

In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral
boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems
constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value
problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

关键词: Fractional calculus, Pseudo solution, boundary value problem, Pettis integrals

Abstract:

Key words: Fractional calculus, Pseudo solution, boundary value problem, Pettis integrals

中图分类号:

26A33

Hussein A.H.Salem . FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL[J]. 数学物理学报(英文版), 2011, 31(2): 661-672.

Hussein A.H.Salem . FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL[J]. Acta mathematica scientia,Series B, 2011, 31(2): 661-672.

参考文献

[1]Ahmad B, Sivasundaram S. Existence of solutions for impulsive integral boundary value problems of fractional order. Nonlinear
Analysis: Hybrid Systems, 2010, 4: 134--141

[2] Ahmad B, Nieto J. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Boundary Value Problems, 2009 (2009), Article ID 708576, 11 pages

[3] Arino O, Gautier S, Penot T P. A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations. Funkcial Ekvac, 1984, 27: 273--279

[4] Bai Z, L"{u}   H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J Math Anal Appl, 2005, 311: 495--505

[5] Ball J M. Weak continuity properties of mapping and semi-groups. Proc Royal Soc Edinburgh Sect, 1973/1974, 72A: 275--280

[6] Bugajewski D, Szulfa S. Kneser's theorem for weak solutions of the Darboux problem in a Banach space. Nonlinear Anal, 1993, 20(2): 169--173

[7] Chandra J, Lakshmikantham V, Mitchell A R. Existence of solutions of boundary value problems for nonlinear second order
systems in Banach spaces. Nonlinear Anal, 1978, 2: 157--168

[8] Cicho\'{n} M. Weak solutions of differential equations in Banach spaces. Discuss Math Diff Incl, 1995, 15: 5--14

[9] Diestel J, Uhl J J Jr. Vector Measures. Math Surveys 15. Providence, R I: Amer Math Soc, 1977

[10] Feng B, Ji D, Ge W. Positive solutions for a class of boundary value problem with integral boundary conditions in Banach spaces. J Comput Appl Math, 2008, 222: 351--363

[11] Feng M, Du B, Ge W. Impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian. Nonlinear Anal, 2009, 70: 3119--3126

[12] Gallardo J M. Second order differential operators with integral boundary conditions and generation of semigroups. Rocky
Mountain J Math, 2000, 30: 1265--1292

[13] Geitz R F. Pettis integration. Proc Amer Math Soc, 1981, 82: 81--86

[14] Geitz R F. Geomerty and the Pettis integral. Trans Amer Math Soc, 1982, 269:  535--548

[15] Gorenflo R,  Vessella S. Abel integral equations//Lecture Notes in Math, Vol 1461. Berlin: Springer, 1991

[16] Liu B. Positive solutions of a nonlinear four-point boundary value problems in Banach spaces. J Math Anal Appl, 2005, 305: 253--276

[17] Lomtatidze A, Malaguti L. On a nonlocal boundary-value problems for second rder nonlinear singular differential equations. Georgian Math J, 2000, 7: 133--154

[18] M\"{o}nch H. Boundary value problems for nonlinear ordinary differential equation of second order in Banach spaces. Nonlinear Anal, 1980, 4: 985--999

[19] O'Regan D. Integral equations in reflexive Banach spaces and the weak topologies. Proc AMS, 1998, 27(5): 607--614

[20] O'Regan D. Weak solutions of ordinary differential equations in Banach spaces. Appl Math Letters, 1999, 12: 101--105

[21] Ozdarska D, Szufla S. Weak solutions for boundary value problem for nonlinear ordinary differential quation of second order in Banach spaces. Math Slovaca, 1993, 43: 301--307

[22] Pettis B J. On integration in vector spaces. Trans Amer Math Soc, 1938, 44: 277--304

[23] Salem H A H, Väth M. An abstract Gronwall lemma and application to global existence results for functional differential and integral
equations of fractional order. J Integral Equations Appl, 2004, 16: 411--429

[24] Salem H A H, El-Sayed A M A,  Moustafa O L. A note on the fractional calculus in Banach spaces. Studia Sci Math Hungar, 2005, 42(2): 115--130

[25] Samko S, Kilbas A, Marichev O. Fractional Integrals andDrivatives. Gordon and Breach Science Publisher, 1993

[26] Satco B. Second order three boundary value problemin Banach spaces via Henstock and Henstock-Kurzweil-Pettis integral. J Math Anal Appl, 2007, 332: 919--933

[27] Szulfa S.Boundary value problems for nonlinear ordinary differential equation of second   order in Banach spaces. Nonlinear Anal, 1984, 4: 1481--1487

[28] Zhang X, Ge W. Positive solutions for a class of boundary-value problems with integral boundary conditions. Comput Math Appl, 2009, 58: 203--215

[29] Zhang X, Feng M, Ge W. Symmetric positive solutions for p-Laplacian fourth-order differential equations with integral boundary conditions. J Comput Appl Math, 2008, 222: 561--573

[30] Zhang X, Yang X, Ge W. Positive solutions of nth-order impulsive boundary value problems with integral boundary conditions in Banach spaces. Nonlinear Anal, 2009, 71: 5930--5945

[31] Zhao Y, Chena H. Existence of multiple positive solutions for m-point boundary value problems in Banach spaces. J Comput Appl Math, 2008, 215: 79--90

FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

FRACTIONAL ORDER BOUNDARY |VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

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]	Alberto CABADA, Nikolay D. DIMITROV. EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS[J]. 数学物理学报(英文版), 2017, 37(4): 911-926.
[2]	侯飞. ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE[J]. 数学物理学报(英文版), 2017, 37(4): 949-964.
[3]	肖羽, 范恩贵, 徐建. THE FOKAS-LENELLS EQUATION ON THE FINITE INTERVAL[J]. 数学物理学报(英文版), 2017, 37(3): 852-876.
[4]	于海波. GLOBAL REGULARITY TO THE 2D INCOMPRESSIBLE MHD WITH MIXED PARTIAL DISSIPATION AND MAGNETIC DIFFUSION IN A BOUNDED DOMAIN[J]. 数学物理学报(英文版), 2017, 37(2): 395-404.
[5]	Nermina MUJAKOVIC, Nelida CRNJARIC-ZIC. GLOBAL SOLUTION TO 1D MODEL OF A COMPRESSIBLE VISCOUS MICROPOLAR HEAT-CONDUCTING FLUID WITH A FREE BOUNDARY[J]. 数学物理学报(英文版), 2016, 36(6): 1541-1576.
[6]	Batirkhan TURMETOV. ON SOME BOUNDARY VALUE PROBLEMS FOR NONHOMOGENOUS POLYHARMONIC EQUATION WITH BOUNDARY OPERATORS OF FRACTIONAL ORDER[J]. 数学物理学报(英文版), 2016, 36(3): 831-846.
[7]	连汝续, 刘健. FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2016, 36(1): 111-123.
[8]	B. J. KADIRKULOV, M. KIRANE. ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION WITH A NONLOCAL BOUNDARY OPERATOR[J]. 数学物理学报(英文版), 2015, 35(5): 970-980.
[9]	刘华. ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS[J]. 数学物理学报(英文版), 2015, 35(5): 1037-1045.
[10]	R. K. SAXENA, D. KUMAR. GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-FUNCTION INVOLVING A GENERAL CLASS OF POLYNOMIALS[J]. 数学物理学报(英文版), 2015, 35(5): 1095-1110.
[11]	Rinaldo M. COLOMBO, Elena ROSSI. RIGOROUS ESTIMATES ON BALANCE LAWS IN BOUNDED DOMAINS[J]. 数学物理学报(英文版), 2015, 35(4): 906-944.
[12]	Eid H. DOHA, Waleed M. ABD-ELHAMEED, Mahmoud A. BASSUONY. ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS[J]. 数学物理学报(英文版), 2015, 35(2): 326-338.
[13]	A.S. BERDYSHEV, A. CABADA, B.Kh. TURMETOV. ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY#br# OPERATOR OF A FRACTIONAL ORDER[J]. 数学物理学报(英文版), 2014, 34(6): 1695-1706.
[14]	韦忠礼. SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS[J]. 数学物理学报(英文版), 2014, 34(6): 1795-1810.
[15]	Rabha W. IBRAHIM, Janusz SOK′O L. ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR[J]. 数学物理学报(英文版), 2014, 34(5): 1417-1426.