{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T22:01:34Z","timestamp":1773007294262,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation\u2019s solution.<\/jats:p>","DOI":"10.3390\/axioms12010053","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T03:27:44Z","timestamp":1672802864000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Iterative Multivalued \u22a5-Preserving Mappings and an Application to Fractional Differential Equation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1274-1936","authenticated-orcid":false,"given":"Muhammad","family":"Nazam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1928-2952","authenticated-orcid":false,"given":"Sumit","family":"Chandok","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"given":"Hamed H. Al","family":"Sulmi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1090\/S0002-9939-1969-0239559-9","article-title":"On nonlinear contractions","volume":"20","author":"Boyd","year":"1969","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1090\/S0002-9939-1962-0148046-1","article-title":"A note on contractive mappings","volume":"13","author":"Rakotch","year":"1962","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_3","first-page":"1","article-title":"Integrable solutions of functional equations","volume":"127","author":"Matkowski","year":"1975","journal-title":"Diss. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1016\/j.na.2011.10.014","article-title":"Fixed point theorems for (\u03b1,\u03c8)-contractive type mappings","volume":"75","author":"Samet","year":"2012","journal-title":"Nonlinear Anal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"793486","DOI":"10.1155\/2012\/793486","article-title":"Generalized (\u03b1,\u03a8)-contractive type mappings and related fixed point theorems with applications","volume":"2012","author":"Karapinar","year":"2012","journal-title":"Abstr. Appl. Anal."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1186\/s13663-016-0553-0","article-title":"The Boyd-Wong idea extended","volume":"2016","author":"Pasick","year":"2016","journal-title":"Fixed Point Theory Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1186\/1687-1812-2012-94","article-title":"Fixed point theory of a new type of contractive mappings in complete metric spaces","volume":"2012","author":"Wardowski","year":"2012","journal-title":"Fixed Point Theory Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s11784-016-0297-9","article-title":"Orthogonal sets: The axiom of choice and proof of a fixed point theorem","volume":"18","author":"Baghani","year":"2016","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_9","first-page":"6692112","article-title":"Fixed point of orthogonal F-Suzuki contraction mapping on O-complete metric spaces with applications","volume":"2021","author":"Beg","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s11784-021-00850-8","article-title":"Multivalued problems vian orthogonal contraction mappings with application to fractional differential equation","volume":"23","author":"Chandok","year":"2021","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s41478-021-00362-1","article-title":"Existence of solution for orthogonal F-contraction mappings via Picard\u2013Jungck sequences","volume":"30","author":"Chandok","year":"2022","journal-title":"J. Anal."},{"key":"ref_12","first-page":"779","article-title":"Weak F-contractions and some fixed point results","volume":"42","author":"Secelean","year":"2016","journal-title":"Bull. Iranian Math. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6615478","DOI":"10.1155\/2020\/6615478","article-title":"Multivalued problems, orthogonal mappings, and fractional integro-differential equation","volume":"2020","author":"Sharma","year":"2020","journal-title":"J. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5291","DOI":"10.3934\/math.2022294","article-title":"A unified fixed point approach to study the existence and uniqueness of solutions to the generalized stochastic functional equation emerging in the psychological theory of learning","volume":"7","author":"Turab","year":"2022","journal-title":"Aims Math."},{"key":"ref_15","first-page":"1399764","article-title":"Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations","volume":"2021","author":"Khan","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Rezapour, S., Deressa, C.T., Hussain, A., Etemad, S., George, R., and Ahmad, B. (2022). A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique. Mathematics, 10.","DOI":"10.3390\/math10040568"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"569","DOI":"10.24193\/fpt-ro.2017.2.45","article-title":"On orthogonal sets and Banach fixed point theorem","volume":"19","author":"Gordji","year":"2017","journal-title":"Fixed Point Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1186\/s13662-021-03405-w","article-title":"Fixed point problems for generalized contractions with applications","volume":"2021","author":"Nazam","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11784-020-0756-1","article-title":"Fixed point theorems for generalized contractive mappings in metric spaces","volume":"22","author":"Proinov","year":"2020","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1186\/1029-242X-2014-38","article-title":"A new generalization of the Banach contraction principle","volume":"2014","author":"Jleli","year":"2014","journal-title":"J. Inequal. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.2298\/FIL1409747M","article-title":"Fixed point of single-valued cyclic weak \u03c6F-contraction mappings","volume":"28","author":"Moradi","year":"2014","journal-title":"Filomat"},{"key":"ref_22","first-page":"1","article-title":"Existence theorems for (\u03a6,\u03a8)-orthogonal interpolative contractions and an application to fractional differential equations","volume":"72","author":"Nazam","year":"2022","journal-title":"Optimization"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"475","DOI":"10.2140\/pjm.1969.30.475","article-title":"Multivalued contraction mappings","volume":"30","author":"Nadler","year":"1969","journal-title":"Pacific J. Math."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1090\/S0002-9939-03-07220-4","article-title":"A fixed point theorem in partially ordered sets and some applications to matrix equations","volume":"132","author":"Ran","year":"2003","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1090\/S0002-9939-1973-0334176-5","article-title":"On contractive mappings","volume":"40","author":"Geraghty","year":"1973","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_26","first-page":"323","article-title":"Theoremi di punto fisso per applicazioni negli spazi metrici","volume":"111","author":"Skof","year":"1977","journal-title":"Atti. Acad. Sci. Torino Cl. Sci. Fis. Mat. Natur."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"305","DOI":"10.5486\/PMD.2016.7308","article-title":"Multivalued F-contractive mappings with a graph and some fixed point results","volume":"88","author":"Acar","year":"2016","journal-title":"Publ. Math. Debr."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"319","DOI":"10.7858\/eamj.2016.024","article-title":"Some fixed point results for multivalued mappings in b-metric spaces","volume":"32","author":"Afshari","year":"2016","journal-title":"East Asian Math. J."},{"key":"ref_29","first-page":"19","article-title":"Generalized contractions and fixed-point theorems","volume":"26","year":"1971","journal-title":"Publ. Inst. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"187","DOI":"10.18514\/MMN.2016.1478","article-title":"Fixed point results for \u03b1-admissible multivalued F-contractions","volume":"17","author":"Durmaz","year":"2016","journal-title":"Miskolc Math. Notes"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2350","DOI":"10.22436\/jnsa.010.05.07","article-title":"Fixed point results for generalized \u0398-contractions","volume":"10","author":"Ahmad","year":"2017","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1186\/s13662-020-2527-0","article-title":"Analyzing transient response of the parallel RCL circuit by using the Caputo-Fabrizio fractional derivative","volume":"2020","author":"Alizadeh","year":"2020","journal-title":"Adv. Differ. Equ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109705","DOI":"10.1016\/j.chaos.2020.109705","article-title":"A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative","volume":"134","author":"Baleanu","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1186\/s13662-020-02544-w","article-title":"Analysis of the model of HIV-1 infection of CD4+ T-cell with a new approach of fractional derivative","volume":"2020","author":"Baleanu","year":"2020","journal-title":"Adv. Differ. Equ."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/1\/53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:57:25Z","timestamp":1760119045000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/1\/53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,3]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["axioms12010053"],"URL":"https:\/\/doi.org\/10.3390\/axioms12010053","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,3]]}}}