{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T11:11:45Z","timestamp":1782126705938,"version":"3.54.5"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T00:00:00Z","timestamp":1679875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012639","name":"Prince Sultan University","doi-asserted-by":"publisher","award":["1"],"award-info":[{"award-number":["1"]}],"id":[{"id":"10.13039\/501100012639","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main results, an analogous representation for the main equation, called a Volterra-type summation equation, is constructed. Two numerical examples are provided to demonstrate the validity of the theoretical findings; no earlier publications have been able to comment on their solutions\u2019 non-oscillatory behavior.<\/jats:p>","DOI":"10.3390\/axioms12040325","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T05:34:30Z","timestamp":1679895270000},"page":"325","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5262-1138","authenticated-orcid":false,"given":"Jehad","family":"Alzabut","sequence":"first","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Department of Industrial Engineering, OST\u0130M Technical University, Ankara 06374, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Said R.","family":"Grace","sequence":"additional","affiliation":[{"name":"Turkey Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Giza 12221, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1310-8323","authenticated-orcid":false,"given":"Jagan Mohan","family":"Jonnalagadda","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, Telangana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9740-3081","authenticated-orcid":false,"given":"Shyam Sundar","family":"Santra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, JIS College of Engineering, Kalyani 741235, West Bengal, India"},{"name":"Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies, Dehradun 248007, Uttarakhand, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8867-0612","authenticated-orcid":false,"given":"Bahaaeldin","family":"Abdalla","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,27]]},"reference":[{"key":"ref_1","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. 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