{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T06:28:40Z","timestamp":1782368920633,"version":"3.54.5"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100010801","name":"Xunta de Galicia","doi-asserted-by":"publisher","award":["EM2014\/032"],"award-info":[{"award-number":["EM2014\/032"]}],"id":[{"id":"10.13039\/501100010801","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Agencia de Investigaci\u00f3n Espa\u00f1ola","award":["MTM2016-75140-P"],"award-info":[{"award-number":["MTM2016-75140-P"]}]},{"name":"PRFU","award":["C00L03EP130220190001"],"award-info":[{"award-number":["C00L03EP130220190001"]}]},{"name":"PRFU","award":["C00L03EP130220190001"],"award-info":[{"award-number":["C00L03EP130220190001"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,7]]},"DOI":"10.1007\/s40314-021-01546-y","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T15:02:50Z","timestamp":1622818970000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Positive solutions for fractional boundary value problems with integral boundary conditions and parameter dependence"],"prefix":"10.1007","volume":"40","author":[{"given":"Hafida","family":"Abbas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3802-7212","authenticated-orcid":false,"given":"Mohammed","family":"Belmekki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1488-935X","authenticated-orcid":false,"given":"Alberto","family":"Cabada","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,6,4]]},"reference":[{"key":"1546_CR1","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, L\u00fc H (2005) Positive solutions for boundary value problem of nonlinear fractional differential equation. J Math Anal Appl 311:495\u2013505","journal-title":"J Math Anal Appl"},{"key":"1546_CR2","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.amc.2013.11.057","volume":"228","author":"A Cabada","year":"2014","unstructured":"Cabada A, Hamdi Z (2014) Nonlinear fractional differential equations with integral boundary value conditions. Appl Math Comput 228:251\u2013257","journal-title":"Appl Math Comput"},{"key":"1546_CR3","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/j.jmaa.2011.11.065","volume":"389","author":"A Cabada","year":"2012","unstructured":"Cabada A, Wang G (2012) Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J Math Anal Appl 389:403\u2013411","journal-title":"J Math Anal Appl"},{"key":"1546_CR4","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1002\/mma.4105","volume":"40","author":"A Cabada","year":"2017","unstructured":"Cabada A, Dimitrijevic S, Tomovic T, Alecsic S (2017) The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions. Math Methods Appl Sci 40:1880\u20131891","journal-title":"Math Methods Appl Sci"},{"key":"1546_CR5","first-page":"217","volume-title":"Scientific computing in chemical engineering II-computational fluid dynamics, reaction engineering and molecular properties","author":"K Diethelm","year":"1999","unstructured":"Diethelm K, Freed AD (1999) On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity. In: Keil F, Mackens W, Voss H, Werther J (eds) Scientific computing in chemical engineering II-computational fluid dynamics, reaction engineering and molecular properties. Springer, Heidelberg, pp 217\u2013224"},{"key":"1546_CR6","doi-asserted-by":"publisher","first-page":"720720","DOI":"10.1186\/1687-2770-2011-720702","volume":"2011","author":"M Feng","year":"2011","unstructured":"Feng M, Zhang X, Ge W (2011) New existence results for higher-order nonlinear fractional differential equations with integral boundary conditions. Bound Value Probl 2011:720720","journal-title":"Bound Value Probl"},{"key":"1546_CR7","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/S0006-3495(95)80157-8","volume":"68","author":"WG Gl\u00f6ckle","year":"1995","unstructured":"Gl\u00f6ckle WG, Nonnenmacher TF (1995) A fractional calculus approach of self-similar protein dynamics. Biophys J 68:46\u201353","journal-title":"Biophys J"},{"issue":"5","key":"1546_CR8","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1007\/s00397-005-0043-5","volume":"45","author":"N Heymans","year":"2006","unstructured":"Heymans N, Podlubny I (2006) Physical interpretation of initial conditions for fractional differential equations with Riemann\u2013Liouville fractional derivatives. Rheol Acta 45(5):765\u2013772","journal-title":"Rheol Acta"},{"key":"1546_CR9","volume-title":"Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies","author":"AA Kilbas","year":"2006","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol 204. Elsevier Science B.V, Amsterdam"},{"key":"1546_CR10","unstructured":"Kiryakova V (1994) Generalized fractional calculus and applications. Pitman research notes in mathematics series, 301. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York"},{"key":"1546_CR11","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/978-3-7091-2664-6_7","volume-title":"Fractals and fractional calculus in continuum mechanics","author":"F Mainardi","year":"1997","unstructured":"Mainardi F (1997) Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri A, Mainardi F (eds) Fractals and fractional calculus in continuum mechanics. Springer, Wien, pp 291\u2013348"},{"key":"1546_CR12","doi-asserted-by":"publisher","first-page":"7180","DOI":"10.1063\/1.470346","volume":"103","author":"F Metzler","year":"1995","unstructured":"Metzler F, Schick W, Kilian HG, Nonnenmacher TF (1995) Relaxation in filled polymers: a fractional calculus approach. J Chem Phys 103:7180\u20137186","journal-title":"J Chem Phys"},{"key":"1546_CR13","volume-title":"An introduction to the fractional calculus and differential equations","author":"KS Miller","year":"1993","unstructured":"Miller KS, Ross B (1993) An introduction to the fractional calculus and differential equations. Wiley, New York"},{"key":"1546_CR14","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1186\/1687-2770-2013-5","volume":"2013","author":"JJ Nieto","year":"2013","unstructured":"Nieto JJ, Pimentel J (2013) Positive solutions of a fractional thermostat model. Bound Value Probl 2013:5","journal-title":"Bound Value Probl"},{"key":"1546_CR15","volume-title":"Fractional differential equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny I (1999) Fractional differential equations. Academic Press, San Diego"},{"key":"1546_CR16","first-page":"367","volume":"5","author":"I Podlubny","year":"2002","unstructured":"Podlubny I (2002) Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calc Appl Anal 5:367\u2013386","journal-title":"Fract Calc Appl Anal"},{"issue":"2","key":"1546_CR17","first-page":"661","volume":"31","author":"HAH Salem","year":"2011","unstructured":"Salem HAH (2011) Fractional order boundary value problem with integral boundary conditions involving Pettis integral. Acta Math Sci Ser B (Engl. Ed.) 31(2):661\u2013672","journal-title":"Acta Math Sci Ser B (Engl. Ed.)"},{"key":"1546_CR18","volume-title":"Fractional integrals and derivatives. Theory and applications","author":"SG Samko","year":"1993","unstructured":"Samko SG, Kilbas AA, Marichev OI (1993) Fractional integrals and derivatives. Theory and applications. Gordon and Breach, Yverdon"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01546-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01546-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01546-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,4]],"date-time":"2023-11-04T14:33:42Z","timestamp":1699108422000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01546-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,4]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["1546"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01546-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,4]]},"assertion":[{"value":"11 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 May 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"158"}}