메뉴 건너뛰기




Volumn 2013, Issue , 2013, Pages

Multiple positive solutions of a singular semipositone integral boundary value problem for fractional q -derivatives equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84874885703     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/643571     Document Type: Article
Times cited : (17)

References (39)
  • 1
    • 0011805878 scopus 로고
    • Q -difference equations
    • 10.2307/2370183 MR1506108
    • Jackson F. H., q -difference equations. American Journal of Mathematics 1910 32 4 305 314 10.2307/2370183 MR1506108
    • (1910) American Journal of Mathematics , vol.32 , Issue.4 , pp. 305-314
    • Jackson, F.H.1
  • 2
    • 0000864250 scopus 로고
    • The general theory of linear q -difference equations
    • 10.2307/2369887 MR1506145
    • Carmichael R. D., The general theory of linear q -difference equations. American Journal of Mathematics 1912 34 2 147 168 10.2307/2369887 MR1506145
    • (1912) American Journal of Mathematics , vol.34 , Issue.2 , pp. 147-168
    • Carmichael, R.D.1
  • 3
    • 0037675743 scopus 로고    scopus 로고
    • New York, NY, USA Springer 10.1007/978-1-4613-0071-7 MR1865777
    • Kac V., Cheung P., Quantum Calculus 2002 New York, NY, USA Springer 10.1007/978-1-4613-0071-7 MR1865777
    • (2002) Quantum Calculus
    • Kac, V.1    Cheung, P.2
  • 4
    • 21844482300 scopus 로고
    • Transformation theory of the q -oscillator
    • 10.1063/1.531057 MR1331280
    • Finkelstein R., Marcus E., Transformation theory of the q -oscillator. Journal of Mathematical Physics 1995 36 6 2652 2672 10.1063/1.531057 MR1331280
    • (1995) Journal of Mathematical Physics , vol.36 , Issue.6 , pp. 2652-2672
    • Finkelstein, R.1    Marcus, E.2
  • 5
    • 21844487732 scopus 로고
    • The spectral problem for the q -Knizhnik-Zamolodchikov equation and continuous q -Jacobi polynomials
    • MR1355617 10.1007/BF02100180
    • Freund P. G. O., Zabrodin A. V., The spectral problem for the q -Knizhnik-Zamolodchikov equation and continuous q -Jacobi polynomials. Communications in Mathematical Physics 1995 173 1 17 42 MR1355617 10.1007/BF02100180
    • (1995) Communications in Mathematical Physics , vol.173 , Issue.1 , pp. 17-42
    • Freund, P.G.O.1    Zabrodin, A.V.2
  • 6
    • 0142160815 scopus 로고    scopus 로고
    • On a q -sequence that generalizes the median Genocchi numbers
    • MR1721730
    • Han G.-N., Zeng J., On a q -sequence that generalizes the median Genocchi numbers. Annales des Sciences Mathématiques du Québec 1999 23 1 63 72 MR1721730
    • (1999) Annales des Sciences Mathématiques du Québec , vol.23 , Issue.1 , pp. 63-72
    • Han, G.-N.1    Zeng, J.2
  • 7
    • 21844503594 scopus 로고
    • Quantum symmetries of q -difference equations
    • 10.1063/1.531017 MR1331313
    • Floreanini R., Vinet L., Quantum symmetries of q -difference equations. Journal of Mathematical Physics 1995 36 6 3134 3156 10.1063/1.531017 MR1331313
    • (1995) Journal of Mathematical Physics , vol.36 , Issue.6 , pp. 3134-3156
    • Floreanini, R.1    Vinet, L.2
  • 8
    • 1642438005 scopus 로고    scopus 로고
    • Variational q-calculus
    • DOI 10.1016/j.jmaa.2003.09.004
    • Bangerezako G., Variational q -calculus. Journal of Mathematical Analysis and Applications 2004 289 2 650 665 10.1016/j.jmaa.2003.09.004 MR2026931 (Pubitemid 38131001)
    • (2004) Journal of Mathematical Analysis and Applications , vol.289 , Issue.2 , pp. 650-665
    • Bangerezako, G.1
  • 9
    • 33646199681 scopus 로고    scopus 로고
    • Second order q -difference equations solvable by factorization method
    • 10.1016/j.cam.2005.06.009 MR2228721
    • Dobrogowska A., Odzijewicz A., Second order q -difference equations solvable by factorization method. Journal of Computational and Applied Mathematics 2006 193 1 319 346 10.1016/j.cam.2005.06.009 MR2228721
    • (2006) Journal of Computational and Applied Mathematics , vol.193 , Issue.1 , pp. 319-346
    • Dobrogowska, A.1    Odzijewicz, A.2
  • 10
    • 69649098522 scopus 로고    scopus 로고
    • Q -difference operators for orthogonal polynomials
    • 10.1016/j.cam.2009.02.044 MR2583013 ZBL1185.39005
    • Ismail M. E. H., Simeonov P., q -difference operators for orthogonal polynomials. Journal of Computational and Applied Mathematics 2009 233 3 749 761 10.1016/j.cam.2009.02.044 MR2583013 ZBL1185.39005
    • (2009) Journal of Computational and Applied Mathematics , vol.233 , Issue.3 , pp. 749-761
    • Ismail, M.E.H.1    Simeonov, P.2
  • 11
    • 84873356580 scopus 로고    scopus 로고
    • Existence results for nonlocal boundary value problems of nonlinear fractional q -difference equations
    • 2012140 10.1186/1687-1847-2012-140
    • Ahmad B., Ntouyas S., Purnaras I., Existence results for nonlocal boundary value problems of nonlinear fractional q -difference equations. Advances in Difference Equations 2012 2012, article 140 10.1186/1687-1847-2012- 140
    • (2012) Advances in Difference Equations
    • Ahmad, B.1    Ntouyas, S.2    Purnaras, I.3
  • 12
    • 77951154272 scopus 로고    scopus 로고
    • Positive solutions of q -difference equation
    • 10.1090/S0002-9939-09-10185-5 MR2587458
    • El-Shahed M., Hassan H. A., Positive solutions of q -difference equation. Proceedings of the American Mathematical Society 2010 138 5 1733 1738 10.1090/S0002-9939-09-10185-5 MR2587458
    • (2010) Proceedings of the American Mathematical Society , vol.138 , Issue.5 , pp. 1733-1738
    • El-Shahed, M.1    Hassan, H.A.2
  • 13
    • 42649085010 scopus 로고    scopus 로고
    • Q -Taylor and interpolation series for Jackson q -difference operators
    • 10.1016/j.jmaa.2008.02.033 MR2416321
    • Annaby M. H., Mansour Z. S., q -Taylor and interpolation series for Jackson q -difference operators. Journal of Mathematical Analysis and Applications 2008 344 1 472 483 10.1016/j.jmaa.2008.02.033 MR2416321
    • (2008) Journal of Mathematical Analysis and Applications , vol.344 , Issue.1 , pp. 472-483
    • Annaby, M.H.1    Mansour, Z.S.2
  • 14
    • 79959203803 scopus 로고    scopus 로고
    • Boundary value problems for q -difference inclusions
    • 292860 10.1155/2011/292860 MR2793778
    • Ahmad B., Ntouyas S. K., Boundary value problems for q -difference inclusions. Abstract and Applied Analysis 2011 2011 15 292860 10.1155/2011/292860 MR2793778
    • (2011) Abstract and Applied Analysis , vol.2011 , pp. 15
    • Ahmad, B.1    Ntouyas, S.K.2
  • 15
    • 33845732591 scopus 로고    scopus 로고
    • Some systems of multivariable orthogonal q -Racah polynomials
    • 10.1007/s11139-006-0259-8 MR2281173
    • Gasper G., Rahman M., Some systems of multivariable orthogonal q -Racah polynomials. The Ramanujan Journal 2007 13 1-3 389 405 10.1007/s11139-006-0259-8 MR2281173
    • (2007) The Ramanujan Journal , vol.13 , Issue.1-3 , pp. 389-405
    • Gasper, G.1    Rahman, M.2
  • 16
    • 1242329948 scopus 로고    scopus 로고
    • Integral inequalities in q -calculus
    • 10.1016/S0898-1221(04)90025-9 MR2047944
    • Gauchman H., Integral inequalities in q -calculus. Computers & Mathematics with Applications 2004 47 2-3 281 300 10.1016/S0898-1221(04)90025-9 MR2047944
    • (2004) Computers & Mathematics with Applications , vol.47 , Issue.2-3 , pp. 281-300
    • Gauchman, H.1
  • 18
    • 78651236363 scopus 로고    scopus 로고
    • Positive solutions for a class of boundary value problems with fractional q -differences
    • 10.1016/j.camwa.2010.11.012 MR2754144
    • Ferreira R. A. C., Positive solutions for a class of boundary value problems with fractional q -differences. Computers & Mathematics with Applications 2011 61 2 367 373 10.1016/j.camwa.2010.11.012 MR2754144
    • (2011) Computers & Mathematics with Applications , vol.61 , Issue.2 , pp. 367-373
    • Ferreira, R.A.C.1
  • 19
    • 84860466937 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional q -difference equation
    • 385459 MR2793792
    • El-Shahed M., Al-Askar F. M., Positive solutions for boundary value problem of nonlinear fractional q -difference equation. ISRN Mathematical Analysis 2011 2011 12 385459 MR2793792
    • (2011) ISRN Mathematical Analysis , vol.2011 , pp. 12
    • El-Shahed, M.1    Al-Askar, F.M.2
  • 20
    • 84865786414 scopus 로고    scopus 로고
    • Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q -differences
    • 10.1007/s12190-012-0551-2 MR2965332
    • Liang S., Zhang J., Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q -differences. Journal of Applied Mathematics and Computing 2012 40 1-2 277 288 10.1007/s12190-012-0551-2 MR2965332
    • (2012) Journal of Applied Mathematics and Computing , vol.40 , Issue.1-2 , pp. 277-288
    • Liang, S.1    Zhang, J.2
  • 21
    • 84860430866 scopus 로고    scopus 로고
    • Positive solutions for a class of higher order boundary value problems with fractional q -derivatives
    • 10.1016/j.amc.2012.03.006 MR2916148
    • Graef J. R., Kong L., Positive solutions for a class of higher order boundary value problems with fractional q -derivatives. Applied Mathematics and Computation 2012 218 19 9682 9689 10.1016/j.amc.2012.03.006 MR2916148
    • (2012) Applied Mathematics and Computation , vol.218 , Issue.19 , pp. 9682-9689
    • Graef, J.R.1    Kong, L.2
  • 23
    • 0003797958 scopus 로고    scopus 로고
    • London, UK Academic Press Mathematics in Science and Engineering MR1658022
    • Podlubny I., Fractional Differential Equations 1999 198 London, UK Academic Press Mathematics in Science and Engineering MR1658022
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 24
    • 74149083504 scopus 로고    scopus 로고
    • Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations
    • 10.1016/j.camwa.2009.06.029 MR2579500 ZBL1189.34014
    • Li C. F., Luo X. N., Zhou Y., Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Computers & Mathematics with Applications 2010 59 3 1363 1375 10.1016/j.camwa.2009.06.029 MR2579500 ZBL1189.34014
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.3 , pp. 1363-1375
    • Li, C.F.1    Luo, X.N.2    Zhou, Y.3
  • 25
    • 79960981115 scopus 로고    scopus 로고
    • Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions
    • 10.1016/j.camwa.2011.04.004 MR2824726 ZBL1228.34021
    • Wang G., Ahmad B., Zhang L., Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions. Computers & Mathematics with Applications 2011 62 3 1389 1397 10.1016/j.camwa.2011.04.004 MR2824726 ZBL1228.34021
    • (2011) Computers & Mathematics with Applications , vol.62 , Issue.3 , pp. 1389-1397
    • Wang, G.1    Ahmad, B.2    Zhang, L.3
  • 26
    • 77955713929 scopus 로고    scopus 로고
    • On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order
    • 10.1016/j.amc.2010.05.080 MR2678559 ZBL1207.45014
    • Ahmad B., Sivasundaram S., On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order. Applied Mathematics and Computation 2010 217 2 480 487 10.1016/j.amc.2010.05.080 MR2678559 ZBL1207.45014
    • (2010) Applied Mathematics and Computation , vol.217 , Issue.2 , pp. 480-487
    • Ahmad, B.1    Sivasundaram, S.2
  • 27
    • 79961013958 scopus 로고    scopus 로고
    • The existence of positive solutions of singular fractional boundary value problems
    • 10.1016/j.camwa.2011.04.048 MR2824725 ZBL1228.34020
    • Staněk S., The existence of positive solutions of singular fractional boundary value problems. Computers & Mathematics with Applications 2011 62 3 1379 1388 10.1016/j.camwa.2011.04.048 MR2824725 ZBL1228.34020
    • (2011) Computers & Mathematics with Applications , vol.62 , Issue.3 , pp. 1379-1388
    • Staněk, S.1
  • 28
    • 80053385595 scopus 로고    scopus 로고
    • Existence of solutions for fractional differential equations with multi-point boundary conditions
    • 10.1016/j.cnsns.2011.07.019 MR2843780 ZBL1245.35153
    • Zhou W.-X., Chu Y.-D., Existence of solutions for fractional differential equations with multi-point boundary conditions. Communications in Nonlinear Science and Numerical Simulation 2012 17 3 1142 1148 10.1016/j.cnsns.2011.07.019 MR2843780 ZBL1245.35153
    • (2012) Communications in Nonlinear Science and Numerical Simulation , vol.17 , Issue.3 , pp. 1142-1148
    • Zhou, W.-X.1    Chu, Y.-D.2
  • 29
    • 84868207724 scopus 로고    scopus 로고
    • Existence of positive solutions for nonlinear fractional functional differential equation
    • 10.1016/j.camwa.2012.01.081 MR2989373
    • Zhao Y., Chen H., Huang L., Existence of positive solutions for nonlinear fractional functional differential equation. Computers & Mathematics with Applications 2012 64 10 3456 3467 10.1016/j.camwa.2012.01.081 MR2989373
    • (2012) Computers & Mathematics with Applications , vol.64 , Issue.10 , pp. 3456-3467
    • Zhao, Y.1    Chen, H.2    Huang, L.3
  • 30
    • 84867579253 scopus 로고    scopus 로고
    • Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives
    • 10.1016/j.amc.2012.07.046 MR2983853
    • Zhang X., Liu L., Wu Y., Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives. Applied Mathematics and Computation 2012 219 4 1420 1433 10.1016/j.amc.2012.07.046 MR2983853
    • (2012) Applied Mathematics and Computation , vol.219 , Issue.4 , pp. 1420-1433
    • Zhang, X.1    Liu, L.2    Wu, Y.3
  • 31
    • 80051790398 scopus 로고    scopus 로고
    • On discrete sequential fractional boundary value problems
    • 10.1016/j.jmaa.2011.06.022 MR2832079 ZBL1236.39008
    • Goodrich C. S., On discrete sequential fractional boundary value problems. Journal of Mathematical Analysis and Applications 2012 385 1 111 124 10.1016/j.jmaa.2011.06.022 MR2832079 ZBL1236.39008
    • (2012) Journal of Mathematical Analysis and Applications , vol.385 , Issue.1 , pp. 111-124
    • Goodrich, C.S.1
  • 32
    • 74149089358 scopus 로고    scopus 로고
    • Positive solutions to singular boundary value problem for nonlinear fractional differential equation
    • 10.1016/j.camwa.2009.06.034 MR2579492 ZBL1189.34050
    • Zhang S., Positive solutions to singular boundary value problem for nonlinear fractional differential equation. Computers & Mathematics with Applications 2010 59 3 1300 1309 10.1016/j.camwa.2009.06.034 MR2579492 ZBL1189.34050
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.3 , pp. 1300-1309
    • Zhang, S.1
  • 33
    • 84871418820 scopus 로고    scopus 로고
    • Existence of solutions for fractional integro-differential equation with multipoint boundary value problem in Banach spaces
    • 172963 10.1155/2012/172963
    • Zhao Y., Huang L., Wang X., Zhu X., Existence of solutions for fractional integro-differential equation with multipoint boundary value problem in Banach spaces. Abstract and Applied Analysis 2012 2012 19 172963 10.1155/2012/172963
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 19
    • Zhao, Y.1    Huang, L.2    Wang, X.3    Zhu, X.4
  • 34
    • 84862776655 scopus 로고    scopus 로고
    • The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives
    • 10.1016/j.amc.2012.02.014 MR2921344
    • Zhang X., Liu L., Wu Y., The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives. Applied Mathematics and Computation 2012 218 17 8526 8536 10.1016/j.amc.2012.02.014 MR2921344
    • (2012) Applied Mathematics and Computation , vol.218 , Issue.17 , pp. 8526-8536
    • Zhang, X.1    Liu, L.2    Wu, Y.3
  • 35
    • 84862289470 scopus 로고    scopus 로고
    • Positive solutions of a fractional boundary value problem with changing sign nonlinearity
    • 149849 10.1155/2012/214042 MR2922915 ZBL1242.35216
    • Wang Y., Liu L., Wu Y., Positive solutions of a fractional boundary value problem with changing sign nonlinearity. Abstract and Applied Analysis 2012 2012 12 149849 10.1155/2012/214042 MR2922915 ZBL1242.35216
    • (2012) Abstract and Applied Analysis , vol.2012 , pp. 12
    • Wang, Y.1    Liu, L.2    Wu, Y.3
  • 36
    • 84974177889 scopus 로고
    • Some fractional q -integrals and q -derivatives
    • MR0218848 10.1017/S0013091500011469
    • Al-Salam W. A., Some fractional q -integrals and q -derivatives. Proceedings of the Edinburgh Mathematical Society 1966-1967 15 135 140 MR0218848 10.1017/S0013091500011469
    • (1966) Proceedings of the Edinburgh Mathematical Society , vol.15 , pp. 135-140
    • Al-Salam, W.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.