{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T17:13:11Z","timestamp":1783012391656,"version":"3.54.6"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"S1","license":[{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s12190-025-02489-x","type":"journal-article","created":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T10:00:15Z","timestamp":1745488815000},"page":"323-340","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Positive bounded solutions for iterative BVP with conformable fractional operator of order in (2,3]"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-4470-4125","authenticated-orcid":false,"given":"Manal","family":"Menchih","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-3641-6449","authenticated-orcid":false,"given":"Hiba","family":"El Asraoui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0001-8574-8488","authenticated-orcid":false,"given":"Khalid","family":"Hilal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-7588-8361","authenticated-orcid":false,"given":"Ahmed","family":"Kajouni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-5450-3127","authenticated-orcid":false,"given":"Mohammad Esmael","family":"Samei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,4,24]]},"reference":[{"key":"2489_CR1","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.cam.2014.01.002","volume":"264","author":"R. Khalil","year":"2014","unstructured":"Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65\u201370 (2014). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.cam.2014.01.002.","journal-title":"J. Comput. Appl. Math."},{"key":"2489_CR2","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.cam.2014.10.016","volume":"279","author":"T. Abdeljawad","year":"2015","unstructured":"Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57\u201366 (2015). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.cam.2014.10.016.","journal-title":"J. Comput. Appl. Math."},{"key":"2489_CR3","first-page":"7","volume":"2015","author":"T. Abdeljawad","year":"2015","unstructured":"Abdeljawad, T., Al Horani, M., Khalil, R.: Conformable fractional semigroups of operators. J. Appl. Psychol. Semigroup Theory Appl. 2015, 7 (2015)","journal-title":"J. Appl. Psychol. Semigroup Theory Appl."},{"issue":"1","key":"2489_CR4","doi-asserted-by":"publisher","first-page":"20240032","DOI":"10.1515\/nleng-2024-0032","volume":"14","author":"S.K. Shah","year":"2025","unstructured":"Shah, S.K., Sarwar, M., Hleili, M., Samei, M.E., Abdeljawad, T.: Generalized [CDATA[$$(\\psi, \\varphi)$$-contraction to investigate Volterra integral inclusions and fractal fractional PDEs in super metric space with numerical experiments. Nonlinear Eng. 14(1), 20240032 (2025). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1515\/nleng-2024-0032.","journal-title":"Nonlinear Eng."},{"key":"2489_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/10.5269\/bspm.66011","volume":"43","author":"L. Karimi","year":"2025","unstructured":"Karimi, L., Samei, M.E., Kaabar, M.K.A.: New generalized results of $$(\\mathfrak{A}$$]][CDATA[,\u00ed)-expansive operators on Hilbert spaces with practical comparison. Boletim da Sociedade Paranaense de Matem\u00e1tica 43, 1\u201314 (2025). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/10.5269\/bspm.66011.","journal-title":"Boletim da Sociedade Paranaense de Matem\u00e1tica"},{"key":"2489_CR6","doi-asserted-by":"publisher","first-page":"3315","DOI":"10.1007\/s41478-024-00802-8","volume":"32","author":"K.J. Ansari","year":"2024","unstructured":"Ansari, K.J., Sharma, V., Samei, M.E.: Charlier polynomial-based modified Kantorovich-Szasz type operators and related approximation outcomes. J. Drug Issues Anal. 32, 3315\u20133333 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s41478-024-00802-8.","journal-title":"J. Drug Issues Anal."},{"key":"2489_CR7","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1186\/s13661-024-01936-1","volume":"2024","author":"S. Nazari","year":"2024","unstructured":"Nazari, S., Samei, M.E.: An existence of the solution for generalized system of fractional q-differential inclusions involving p-Laplacian operator and sequential derivatives. Bound. Value. Probl. 2024, 117 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1186\/s13661-024-01936-1.","journal-title":"Bound. Value. Probl."},{"key":"2489_CR8","doi-asserted-by":"publisher","first-page":"17","DOI":"10.28919\/ejma.2024.4.17","volume":"4","author":"A. Boutiara","year":"2024","unstructured":"Boutiara, A., Kaabar, M.K.A., Samei, M.E.: A study on fractional hybrid Sturm-Liouville and Langevin differential equations and inclusions in the frame of \u03c8-Hilfer operator. Eur J Public Health Math. Appl. 4, 17 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.28919\/ejma.2024.4.17.","journal-title":"Eur J Public Health Math. Appl."},{"key":"2489_CR9","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1186\/s13660-024-03158-6","volume":"2024","author":"G.K. Khokhar","year":"2024","unstructured":"Khokhar, G.K., Patel, D.K., Patle, P.R., Samei, M.E.: Optimal solution of $$(k, \\psi)$$-Hilfer fractional differential equation by $$\\mathcal{A}$$-condensing operators. J. Inequal. Appl. 2024, 79 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1186\/s13660-024-03158-6.","journal-title":"J. Inequal. Appl."},{"issue":"3\u20134","key":"2489_CR10","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1177\/10775463221149232","volume":"30","author":"H.A. Hammad","year":"2024","unstructured":"Hammad, H.A., Rashwan, R.A., Nafea, A., Samei, M.E., Noeiaghdam, S.: Stability analysis for a tripled system of fractional pantograph differential equations with nonlocal conditions. J. Vib. Control 30(3\u20134), 632\u2013647 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1177\/10775463221149232.","journal-title":"J. Vib. Control"},{"key":"2489_CR11","volume-title":"International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics","author":"D.R. Driver","year":"1963","unstructured":"Driver, D.R.: A functional differential system of neutral type arising in a two-body problem of classical electrodynamics. In: International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics. Springer, London (1963)"},{"key":"2489_CR12","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1038\/s41598-024-51415-x","volume":"14","author":"B. Mohammadaliee","year":"2024","unstructured":"Mohammadaliee, B., Roomi, V., Samei, M.E.: SEIQR model for analyzing COVID-19 with vaccination via conformable fractional derivative and numerical simulation. Sci. Rep. 14, 723 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1038\/s41598-024-51415-x.","journal-title":"Sci. Rep."},{"key":"2489_CR13","doi-asserted-by":"publisher","first-page":"390","DOI":"10.3390\/axioms11080390","volume":"11","author":"X. Wang","year":"2022","unstructured":"Wang, X., Berhail, A., Tabouche, N., Matar, M.M., Samei, M.E., Kaabar, M.K.A., Yue, X.G.: A novel investigation of non-periodic snap bvp in the g-Caputo sense. Axioms 11, 390 (2022). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/axioms11080390.","journal-title":"Axioms"},{"key":"2489_CR14","doi-asserted-by":"publisher","unstructured":"Mohammadaliee, B., Samei, M.E., Roomi, V., Rezapour, S.: Optimal control strategies and cost-effectiveness analysis for infectious diseases under fractal-fractional derivative: a case study of cholera outbreak. J. Appl. Math. Comput. 2025 (2025). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12190-024-02331-w.","DOI":"10.1007\/s12190-024-02331-w"},{"issue":"3","key":"2489_CR15","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1016\/0022-0396(84)90150-5","volume":"54","author":"E. Eder","year":"1984","unstructured":"Eder, E.: The functional-differential equation $$x^{\\prime}(t) = x(x(t))$$. J. Differ. Equ. 54(3), 390\u2013400 (1984). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/0022-0396(84)90150-5.","journal-title":"J. Differ. Equ."},{"key":"2489_CR16","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1155\/2022\/6713533","volume":"2022","author":"S. Rezapour","year":"2022","unstructured":"Rezapour, S., Boulfoul, A., Tellab, B., Samei, M.E., Etemad, S., George, R.: Fixed point theory and the Caputo-Liouville integro-differential FBVP with multiple nonlinear terms. J. Educ. Chang. Funct. Space 2022, 18 (2022). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1155\/2022\/6713533.","journal-title":"J. Educ. Chang. Funct. Space"},{"key":"2489_CR17","unstructured":"Hale, J.K.: Functional differential equations. In: Analytic Theory of Differential Equations: The Proceedings of the Conference at Western Michigan University, Kalamazoo, Springer, Berlin Heidelberg (2006)"},{"key":"2489_CR18","first-page":"252","volume":"3","author":"V.R. Petahov","year":"1965","unstructured":"Petahov, V.R.: On a boundary value problem. Trudy sem. teorii diff. uravn. otklon. 3, 252\u2013255 (1965)","journal-title":"Trudy sem. teorii diff. uravn. otklon."},{"issue":"1","key":"2489_CR19","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s12190-020-01406-8","volume":"65","author":"S. Cheraiet","year":"2021","unstructured":"Cheraiet, S., Bouakkaz, A., Khemis, R.: Bounded positive solutions of an iterative three-point boundary-value problem with integral boundary condtions. J. Appl. Math. Comput. 65(1), 597\u2013610 (2021). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12190-020-01406-8.","journal-title":"J. Appl. Math. Comput."},{"key":"2489_CR20","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s12346-024-01132-7","volume":"23","author":"M. Menchih","year":"2024","unstructured":"Menchih, M., Hilal, K., Kajouni, A., Samei, M.E.: Chaotic dynamics of conformable maturity-structured cell population models. Qual. Theory Dyn. Syst. 23, 271 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12346-024-01132-7.","journal-title":"Qual. Theory Dyn. Syst."},{"issue":"3","key":"2489_CR21","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s12346-024-00970-9","volume":"23","author":"M.M. Matar","year":"2024","unstructured":"Matar, M.M., Samei, M.E., Etemad, S., Amara, A., Rezapour, S., Alzabut, J.: Stability analysis and existence criteria with numerical illustrations to fractional jerk differential system involving generalized Caputo derivative. Qual. Theory Dyn. Syst. 23(3), 111 (2024). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12346-024-00970-9.","journal-title":"Qual. Theory Dyn. Syst."},{"key":"2489_CR22","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1186\/s13660-022-02764-6","volume":"2022","author":"A. Boutiara","year":"2022","unstructured":"Boutiara, A., Benbachir, M., Kaabar, M.K.A., Mart\u00ednez Gonz\u00e1lez, F., Samei, M.E., Kaplan, M.: Explicit iteration and unbounded solutions for fractional q-difference equations with boundary conditions on an infinite interval. J. Inequal. Appl. 2022, 29 (2022). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1186\/s13660-022-02764-6.","journal-title":"J. Inequal. Appl."},{"key":"2489_CR23","doi-asserted-by":"publisher","first-page":"194","DOI":"10.3390\/fractalfract5040194","volume":"5","author":"A. Boutiara","year":"2021","unstructured":"Boutiara, A., Benbachir, M., Alzabut, J., Samei, M.E.: Monotone iterative and upper-lower solutions techniques for solving nonlinear \u03c8-Caputo fractional boundary value problem. Fractal Fract. 5, 194 (2021). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/fractalfract5040194.","journal-title":"Fractal Fract."},{"issue":"10","key":"2489_CR24","doi-asserted-by":"publisher","first-page":"3351","DOI":"10.3934\/dcdss.2020440","volume":"14","author":"T. Abdeljawad","year":"2021","unstructured":"Abdeljawad, T., Samei, M.E.: Applying quantum calculus for the existence of solution of q-integro-differential equations with three criteria. Discrete Contin. Dyn. Syst. Ser. S 14(10), 3351\u20133386 (2021). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3934\/dcdss.2020440.","journal-title":"Discrete Contin. Dyn. Syst. Ser. S"},{"key":"2489_CR25","doi-asserted-by":"publisher","first-page":"110426","DOI":"10.1016\/j.chaos.2020.110426","volume":"141","author":"M. Chaudhary","year":"2020","unstructured":"Chaudhary, M., Kumar, R., Singh, M.K.: Fractional convection-dispersion equation with conformable derivative approach. Chaos Solit. Fractals 141, 110426 (2020). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.chaos.2020.110426.","journal-title":"Chaos Solit. Fractals"},{"key":"2489_CR26","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.chaos.2020.110426","volume":"126","author":"A. Atangana","year":"2019","unstructured":"Atangana, A., Khan, M.A.: Validity of fractal derivative to capturing chaotic attractors. Chaos Solit. Fractals 126, 50\u201359 (2019). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1016\/j.chaos.2020.110426.","journal-title":"Chaos Solit. Fractals"},{"issue":"2","key":"2489_CR27","doi-asserted-by":"publisher","first-page":"115","DOI":"10.18576\/pfda\/020204","volume":"2","author":"O.S. Iyiola","year":"2016","unstructured":"Iyiola, O.S., Nwaeze, E.R.: Some new results on the new conformable fractional calculus with application using d\u2019alambert approach. Progr. Fract. Differ. Appl. 2(2), 115\u2013122 (2016)","journal-title":"Progr. Fract. Differ. Appl."},{"key":"2489_CR28","volume-title":"Fixed Point Theorems","author":"D.R. Smart","year":"1980","unstructured":"Smart, D.R.: Fixed Point Theorems. Cambridge University Press, Cambridge (1980)"},{"issue":"2","key":"2489_CR29","doi-asserted-by":"publisher","first-page":"1903","DOI":"10.1007\/s12190-022-01820-0","volume":"69","author":"R. Khemis","year":"2023","unstructured":"Khemis, R.: Existence, uniqueness and stability of positive periodic solutions for an iterative Nicholson\u2019s blowflies equation. J. Appl. Math. Comput. 69(2), 1903\u20131916 (2023). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12190-022-01820-0.","journal-title":"J. Appl. Math. Comput."},{"issue":"3","key":"2489_CR30","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1007\/s12190-022-01820-0","volume":"17","author":"A. Bouakkaz","year":"2017","unstructured":"Bouakkaz, A., Ardjouni, A., Djoudi, A.: Existence of positive periodic solutions for a second-order nonlinear neutral differential equation by the Krasnoselskii\u2019s fixed point theorem. Nonlinear Dyn. Syst. Theory 17(3), 230\u2013238 (2017). https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12190-022-01820-0.","journal-title":"Nonlinear Dyn. Syst. Theory"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02489-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/article\/10.1007\/s12190-025-02489-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02489-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T13:15:36Z","timestamp":1757423736000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/link.springer.com\/10.1007\/s12190-025-02489-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,24]]},"references-count":30,"journal-issue":{"issue":"S1","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["2489"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s12190-025-02489-x","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,24]]},"assertion":[{"value":"24 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}