{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,31]],"date-time":"2026-05-31T11:00:39Z","timestamp":1780225239480,"version":"3.54.0"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.cam.2026.117769","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T22:01:27Z","timestamp":1777932087000},"page":"117769","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Critical parameter regimes for positivity in nonlinear delta fractional models"],"prefix":"10.1016","volume":"487","author":[{"given":"Meraa","family":"Arab","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117769_bib0001","series-title":"Fractional Calculus","author":"Agarwal","year":"2018"},{"key":"10.1016\/j.cam.2026.117769_bib0002","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2021.105904","article-title":"Variable-order fractional calculus: a change of perspective","volume":"102","author":"Garrappa","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.cam.2026.117769_bib0003","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.3390\/stats7040074","article-title":"Statistical distribution theory and fractional calculus","volume":"7","author":"Mathai","year":"2024","journal-title":"Stats"},{"key":"10.1016\/j.cam.2026.117769_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.ins.2025.122907","article-title":"Enhancing image encryption through fractional-order chaotic systems: a comparative analysis of six diverse models","volume":"730","author":"\u00c7elik","year":"2026","journal-title":"Inf. Sci."},{"key":"10.1016\/j.cam.2026.117769_bib0005","doi-asserted-by":"crossref","first-page":"7688","DOI":"10.1002\/mma.7083","article-title":"Discrete generalized fractional operators defined using h-discrete Mittag-Leffler kernels and applications to AB fractional difference systems","volume":"46","author":"Mohammed","year":"2020","journal-title":"Math. Meth. Appl. Sci."},{"key":"10.1016\/j.cam.2026.117769_bib0006","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2021.107049","article-title":"Discrete rogue waves and blow-up from solitons of a nonisospectral semi-discrete nonlinear Schr\u00f6dinger equation","volume":"116","author":"Silem","year":"2021","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.cam.2026.117769_bib0007","series-title":"Discrete Fractional Calculus","author":"Goodrich","year":"2015"},{"key":"10.1016\/j.cam.2026.117769_bib0008","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1155\/2013\/406910","article-title":"On delta and nabla Caputo fractional differences and dual identities","volume":"2013","author":"Abdeljawad","year":"2013","journal-title":"Discrete Dyn. Nat. Soc."},{"key":"10.1016\/j.cam.2026.117769_bib0009","doi-asserted-by":"crossref","first-page":"18127","DOI":"10.3934\/math.2022997","article-title":"A relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results","volume":"7","author":"Guirao","year":"2022","journal-title":"AIMS Math."},{"key":"10.1016\/j.cam.2026.117769_bib0010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40304-014-0027-9","article-title":"Solutions of nabla fractional difference equations using N-transforms","volume":"2","author":"Jagan Mohan","year":"2014","journal-title":"Commun. Math. Stat."},{"key":"10.1016\/j.cam.2026.117769_bib0011","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3390\/fractalfract9020131","article-title":"Existence of positive solutions for a class of nabla fractional boundary value problems","volume":"9","author":"Dimitrov","year":"2025","journal-title":"Fractal Fract."},{"key":"10.1016\/j.cam.2026.117769_bib0012","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-025-32192-7","article-title":"Investigation of a Lyapunov delta-type inequality with respect to a discrete fractional Green\u2019s function","author":"Mohammed","year":"2025","journal-title":"Sci. Rep."},{"key":"10.1016\/j.cam.2026.117769_bib0013","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.jmaa.2011.06.022","article-title":"On discrete sequential fractional boundary value problems","volume":"385","author":"Goodrich","year":"2012","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.cam.2026.117769_bib0014","series-title":"Green\u2019s Functions and Lyapunov Inequalities for Nabla Caputo Boundary Value Problems","author":"Ikram","year":"2018"},{"key":"10.1016\/j.cam.2026.117769_bib0015","doi-asserted-by":"crossref","first-page":"991","DOI":"10.3390\/sym16080991","article-title":"Maximum and minimum results for the Green\u2019s functions in delta fractional difference settings","volume":"16","author":"Mohammed","year":"2024","journal-title":"Symmetry"},{"key":"10.1016\/j.cam.2026.117769_bib0016","article-title":"Uniqueness results based on delta fractional operators for certain boundary value problems","volume":"30","author":"Mohammed","year":"2024","journal-title":"Fractals"},{"key":"10.1016\/j.cam.2026.117769_bib0017","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.aej.2024.11.072","article-title":"Positivity and uniqueness of solutions for Riemann-Liouville fractional problem of delta types","volume":"114","author":"Srivastava","year":"2025","journal-title":"Alex. Eng. J."},{"key":"10.1016\/j.cam.2026.117769_bib0018","doi-asserted-by":"crossref","first-page":"857","DOI":"10.3906\/mat-1904-29","article-title":"Existence and uniqueness of solutions for nonlinear Caputo fractional difference equations","volume":"44","author":"Chen","year":"2020","journal-title":"Turk. J. Math."},{"key":"10.1016\/j.cam.2026.117769_bib0019","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1007\/s11071-021-06372-9","article-title":"On a problem of linearized stability for fractional difference equations","volume":"104","author":"\u010cerm\u00e1k","year":"2021","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.cam.2026.117769_bib0020","first-page":"149","article-title":"Analysis of a system of nonlinear fractional nabla difference equations","volume":"5","author":"Jonnalagadda","year":"2015","journal-title":"Int. J. Dyn. Syst. Differ. Equ."},{"key":"10.1016\/j.cam.2026.117769_bib0021","first-page":"85","article-title":"Lyapunov-type inequalities for discrete Riemann\u2013Liouville fractional boundary value problems","volume":"13","author":"Jonnalagadda","year":"2018","journal-title":"Int. J. Difference Equ."},{"key":"10.1016\/j.cam.2026.117769_bib0022","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1016\/j.amc.2014.01.132","article-title":"Lyapunov-type inequality for higher order difference equations","volume":"232","author":"Liu","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117769_bib0023","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.aml.2016.10.013","article-title":"Lyapunov-type inequalities for fractional partial differential equations","volume":"66","author":"Jleli","year":"2017","journal-title":"Appl. Math. Lett."},{"issue":"256","key":"10.1016\/j.cam.2026.117769_bib0024","article-title":"A coupled system of fractional difference equations with nonlocal fractional sum boundary conditions on the discrete half-Line","volume":"7","author":"Soontharanon","year":"2019","journal-title":"Mathematics"},{"key":"10.1016\/j.cam.2026.117769_bib0025","series-title":"Fixed Point Theory and Applications","author":"Agarwal","year":"2001"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726004115?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726004115?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,31]],"date-time":"2026-05-31T10:04:12Z","timestamp":1780221852000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726004115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":25,"alternative-id":["S0377042726004115"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117769","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Critical parameter regimes for positivity in nonlinear delta fractional models","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117769","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117769"}}