{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:13:29Z","timestamp":1767705209670,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T00:00:00Z","timestamp":1556150400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No. 11761038","No. 11761039"],"award-info":[{"award-number":["No. 11761038","No. 11761039"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation of Jiangxi Province of China","award":["No. 20171BAB202010"],"award-info":[{"award-number":["No. 20171BAB202010"]}]},{"name":"the Science and Technology Project of Department of Education of Jiangxi Province","award":["No. GJJ180583"],"award-info":[{"award-number":["No. GJJ180583"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2019,10]]},"DOI":"10.1007\/s12190-019-01264-z","type":"journal-article","created":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T06:05:32Z","timestamp":1556172332000},"page":"559-572","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["The existence of solutions for mixed fractional resonant boundary value problem with p(t)-Laplacian operator"],"prefix":"10.1007","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7898-7907","authenticated-orcid":false,"given":"Xiaosong","family":"Tang","sequence":"first","affiliation":[]},{"given":"Xinchang","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Zhiwei","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Peichang","family":"Ouyang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,4,25]]},"reference":[{"key":"1264_CR1","volume-title":"Letter from Hanover, Germany, September 30, 1695, to G","author":"GW Leibnitz","year":"1849","unstructured":"Leibnitz, G.W.: Letter from Hanover, Germany, September 30, 1695, to G. A L\u2019Hospital, Leibnizen Mathematische Schriften, Olms, Hildesheim, Germany (1849)"},{"key":"1264_CR2","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equation","author":"KS Miller","year":"1993","unstructured":"Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equation. Wiley, New York (1993)"},{"key":"1264_CR3","volume-title":"Srivasfava, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies","author":"AA Kibas","year":"2006","unstructured":"Kibas, A.A., Anatoly, A.: Srivasfava, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier Science BV, Amsterdam (2006)"},{"volume-title":"Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering","year":"2007","unstructured":"Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007)","key":"1264_CR4"},{"key":"1264_CR5","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1016\/j.jmaa.2005.02.052","volume":"311","author":"Z Bai","year":"2005","unstructured":"Bai, Z., Lu, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495\u2013505 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"1264_CR6","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.jmaa.2010.04.034","volume":"371","author":"RP Agarwal","year":"2010","unstructured":"Agarwal, R.P., O\u2019Regan, D., Stanek, S.: Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations. J. Math. Anal. Appl. 371, 57\u201368 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"1264_CR7","doi-asserted-by":"publisher","first-page":"3232","DOI":"10.1016\/j.na.2010.07.003","volume":"73","author":"Z Wei","year":"2010","unstructured":"Wei, Z., Dong, W., Che, J.: Periodic boundary value problems for fractional differential equations involving a Riemann\u2013Liouville fractional derivative. Nonlinear Anal. TMA 73, 3232\u20133238 (2010)","journal-title":"Nonlinear Anal. TMA"},{"issue":"1","key":"1264_CR8","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1186\/s13661-015-0408-3","volume":"2015","author":"H Jin","year":"2015","unstructured":"Jin, H., Liu, W.: On the periodic boundary value problem for Duffing type fractional differential equation with p-Laplacian operator. Bound. Value Probl. 2015(1), 144 (2015)","journal-title":"Bound. Value Probl."},{"issue":"2","key":"1264_CR9","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s11565-013-0181-0","volume":"60","author":"X Tang","year":"2014","unstructured":"Tang, X.: Existence and uniqueness of nontrivial solutions for eigenvalue boundary value problem of nonlinear fractional differential equation. Annali dell\u2019Universita di Ferrara 60(2), 429\u2013445 (2014)","journal-title":"Annali dell\u2019Universita di Ferrara"},{"key":"1264_CR10","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.aml.2017.08.008","volume":"76","author":"G Wang","year":"2018","unstructured":"Wang, G.: Twin iterative positive solutions of fractional q-difference Schr\u00f6dinger equations. Appl. Math. Lett. 76, 103\u2013109 (2018)","journal-title":"Appl. Math. Lett."},{"issue":"708576","key":"1264_CR11","first-page":"11","volume":"2009","author":"B Ahmad","year":"2009","unstructured":"Ahmad, B., Nieto, J.J.: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Bound. Value Probl. 2009(708576), 11 (2009)","journal-title":"Bound. Value Probl."},{"key":"1264_CR12","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/j.jmaa.2008.11.082","volume":"353","author":"X Zhang","year":"2009","unstructured":"Zhang, X., Feng, M., Ge, W.: Existence result of second-order differential equations with integral boundary conditions at resonance. J. Math. Anal. Appl. 353, 311\u2013319 (2009)","journal-title":"J. Math. Anal. Appl."},{"key":"1264_CR13","first-page":"1","volume":"135","author":"N Kosmatov","year":"2010","unstructured":"Kosmatov, N.: A boundary value problem of fractional order at resonance. Electron. J. Differ. Equ. 135, 1\u201310 (2010)","journal-title":"Electron. J. Differ. Equ."},{"issue":"720702","key":"1264_CR14","first-page":"20","volume":"2011","author":"M Feng","year":"2011","unstructured":"Feng, M., Zhang, X., Ge, W.: New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions. Bound. Value Probl. 2011(720702), 20 (2011)","journal-title":"Bound. Value Probl."},{"issue":"3","key":"1264_CR15","first-page":"747","volume":"36","author":"Z Hu","year":"2013","unstructured":"Hu, Z., Liu, W., Chen, T.: Two-point boundary value problems for fractional differential equations at resonance. Bull. Malays. Math. Sci. Soc. 36(3), 747\u2013755 (2013)","journal-title":"Bull. Malays. Math. Sci. Soc."},{"issue":"1\u20132","key":"1264_CR16","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s12190-012-0598-0","volume":"41","author":"X Tang","year":"2013","unstructured":"Tang, X., Yan, C., Liu, Q.: Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance. J. Appl. Math. Comput. 41(1\u20132), 119\u2013131 (2013)","journal-title":"J. Appl. Math. Comput."},{"issue":"1\u20132","key":"1264_CR17","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s12190-015-0896-4","volume":"51","author":"X Tang","year":"2016","unstructured":"Tang, X.: Existence of solutions of four-point boundary value problems for fractional differential equations at resonance. J. Appl. Math. Comput. 51(1\u20132), 145\u2013160 (2016)","journal-title":"J. Appl. Math. Comput."},{"issue":"1","key":"1264_CR18","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1186\/s13661-018-0986-y","volume":"2018","author":"W Jiang","year":"2018","unstructured":"Jiang, W., Kosmatov, N.: Resonant p-Laplacian problems with functional boundary conditions. Bound. Value Probl. 2018(1), 72 (2018)","journal-title":"Bound. Value Probl."},{"issue":"145","key":"1264_CR19","first-page":"26","volume":"2018","author":"P Li","year":"2018","unstructured":"Li, P., Feng, M.: Denumerably many positive solutions for a n-dimensional higher-order singular fractional differential system. Adv. Differ. Equ. 2018(145), 26 (2018)","journal-title":"Adv. Differ. Equ."},{"key":"1264_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0104029","volume-title":"Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics","author":"M Ru\u0307\u017ei\u010dka","year":"2000","unstructured":"Ru\u0307\u017ei\u010dka, M.: Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics. Springer, Berlin (2000)"},{"key":"1264_CR21","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1137\/050624522","volume":"66","author":"Y Chen","year":"2006","unstructured":"Chen, Y., Levine, S., Rao, M.: Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66, 1383\u20131406 (2006)","journal-title":"SIAM J. Appl. Math."},{"key":"1264_CR22","first-page":"675","volume":"50","author":"VV Zhikov","year":"1986","unstructured":"Zhikov, V.V.: Averaging of functionals of the calculus of variations and elasticity theory. Izv. Akad. Nauk SSSR Ser. Mat. 50, 675\u2013710 (1986). (Russian)","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"1264_CR23","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.jmaa.2003.11.020","volume":"302","author":"X Fan","year":"2005","unstructured":"Fan, X., Zhang, Q., Zhao, D.: Eigenvalues of p(x)-Laplacian Dirichlet problem. J. Math. Anal. Appl. 302, 306\u2013317 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"1264_CR24","doi-asserted-by":"publisher","first-page":"5000","DOI":"10.22436\/jnsa.009.07.04","volume":"9","author":"T Shen","year":"2016","unstructured":"Shen, T., Liu, W.: Existence of solutions for fractional integral boundary value problems with p(t)-Laplacian operator. J. Nonlinear Sci. Appl. 9, 5000\u20135010 (2016)","journal-title":"J. Nonlinear Sci. Appl."},{"key":"1264_CR25","doi-asserted-by":"publisher","first-page":"2950","DOI":"10.1016\/j.na.2009.11.038","volume":"72","author":"Q Zhang","year":"2010","unstructured":"Zhang, Q., Wang, Y., Qiu, Z.: Existence of solutions and boundary asymptotic behavior of p(r)-Laplacian equation multi-point boundary value problems. Nonlinear Anal. 72, 2950\u20132973 (2010)","journal-title":"Nonlinear Anal."},{"key":"1264_CR26","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/040","volume-title":"Topological Degree Methods in Nonlinear Boundary Value Problems. CBMS Regional Conference Series in Mathematics","author":"J Mawhin","year":"1979","unstructured":"Mawhin, J.: Topological Degree Methods in Nonlinear Boundary Value Problems. CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence (1979)"},{"key":"1264_CR27","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.jmaa.2011.05.082","volume":"384","author":"C Bai","year":"2011","unstructured":"Bai, C.: Impulsive periodic boundary value problems for fractional differential equation involving Riemann\u2013Liouville sequential fractional derivative. J. Math. Anal. Appl. 384, 211\u2013231 (2011)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-019-01264-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12190-019-01264-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-019-01264-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T23:25:30Z","timestamp":1587684330000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12190-019-01264-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,25]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["1264"],"URL":"https:\/\/doi.org\/10.1007\/s12190-019-01264-z","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2019,4,25]]},"assertion":[{"value":"26 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 April 2019","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}