Advances in Difference Equations

About Advances in Difference Equations

Advances in Difference Equations — Journal Profile

Advances in Difference Equations was a peer-reviewed, fully open access mathematics journal published by Springer Nature through its SpringerOpen imprint, carrying the print ISSN 1687-1839 and the electronic ISSN 1687-1847 — the pair stored on this JournalsWorld record and confirmed by the journal's own Directory of Open Access Journals record. It published original research and survey articles on difference equations, on abstract, functional and fractional differential equations, and on their applications across science and engineering. The journal ran under this title from 2004 to the end of 2021, and from 1 January 2022 it continued under a new title, Advances in Continuous and Discrete Models: Theory and Modern Applications, with a broadened scope. This profile describes the journal under its original title — the title attached to these ISSNs and to the large archive of articles that carry them — and explains the change of title in full, because the single most useful thing a profile of this journal can do is stop readers, authors and librarians from confusing the archive, the successor, and the similarly named journals around them.

The identity anchors are exact. The DOAJ record for the title gives pISSN 1687-1839 and eISSN 1687-1847, names SpringerOpen as publisher, and dates the journal's open access start to 2004. OpenAlex, resolving the ISSN through its ISSN endpoint to source S169017477, records the same ISSN pair, a first publication year of 2004 and a last publication year of 2021 under this title — the bibliographic fingerprint of a journal that completed its final volume in 2021 and then continued under a new name rather than ceasing. Article DOIs from the Springer period follow the patterns 10.1186/1687-1847-year-article in the earlier SpringerOpen years and 10.1186/s13662-year-article later, 13662 being the journal's number in Springer's system; any article carrying those patterns and these ISSNs belongs to this journal's archive.

At a Glance

History: From Launch to SpringerOpen

The journal began publishing in 2004 as an open access title devoted to a field that was expanding quickly. Difference equations — the discrete analogues of differential equations, governing systems that change step by step rather than continuously — sit underneath population models, economic dynamics, numerical schemes, control systems and much of computational mathematics, and the fractional and functional differential equations in the journal's stated scope were attracting a fast-growing research community in the same years. The journal's own description of its aims, carried in its editorial announcements, was to report new developments in the theory of difference equations, abstract, functional and fractional differential equations, and their applications in all fields, accepting high-quality original research and survey articles of exceptional merit.

An editorial announcement published in the journal records its transfer to Springer, to continue publication as part of the SpringerOpen range of fully open access journals, with the founding editor-in-chief continuing in the role and with the journal's existing coverage in indexing and abstracting services continuing uninterrupted. Under SpringerOpen the journal became a high-volume continuous-publication title: articles appeared one by one through the year rather than in assembled issues, each carrying its own article number inside an annual volume — a pattern visible in citations such as Advances in Difference Equations 2013, 354, or 2021, 518. By the time the title closed, OpenAlex had attached 4,884 works to its record — a substantial archive for a specialist mathematics journal, and the foundation of its citation record.

The 2022 Change of Title

Springer Nature announced in 2021 that the journal would begin a new chapter. From 1 July 2021, new submissions were considered for the successor title, and Advances in Difference Equations completed its last volume under its original aims and scope at the end of 2021. From 1 January 2022 the journal has published as Advances in Continuous and Discrete Models: Theory and Modern Applications, led, at the transition, by three editors-in-chief named in the announcement — Harbir Antil of George Mason University, Xue-Cheng Tai of Hong Kong Baptist University, and Enrique Zuazua of Friedrich-Alexander-Universität Erlangen-Nürnberg. The successor's aims, as its own journal pages state them, widen the old remit considerably: alongside differential equations it welcomes scientific computing and machine learning, data-driven modelling, numerical analysis, control, optimisation, and computational tools for managing uncertainty and randomness, organised in sections that include numerical analysis and scientific computing, partial differential equations and mathematical physics, control, stochastic modelling, and mathematical biology and bioengineering.

For practical purposes the change of title means three things. First, the archive stays where it is: articles published from 2004 to 2021 keep the journal title Advances in Difference Equations, its ISSNs and its DOIs, and should be cited exactly as published. Second, new manuscripts go to the successor title, which has its own ISSN, 2731-4235, recorded on its separate JournalsWorld record — authors should not submit to the old title expecting publication under it. Third, metrics do not transfer automatically: citation counts, rankings and index coverage attach to specific titles and ISSNs, and anyone evaluating the successor should expect its record to be built from 2022 onward, even though it inherits the earlier journal's community, publisher and archive readership. This JournalsWorld profile therefore reports the original title's own record, attributed to its own sources, and treats the successor as the separate — if directly descended — publication that it bibliographically is.

Scope in Its Own Terms

Within its 2004–2021 run, the journal's centre of gravity was the theory and application of discrete and fractional models. Its pages carried work on boundary value problems for difference and q-difference equations, stability and oscillation theory, fractional calculus and fractional differential equations, impulsive equations, equations on time scales, and the application of those methods to biological, physical and engineering systems — the neighbouring topics visible in the journal's most-cited articles, which range from fractional boundary value problems to global dynamics of rational difference equations. Survey articles of exceptional merit were explicitly welcomed alongside original research, and the journal's large annual article counts in its later SpringerOpen years made it one of the main open venues in its niche: a place where a solid, technically complete paper on a difference-equation problem could expect a quick and impartial review process, in the words of its own editorial description, followed by immediate online appearance on acceptance.

Metrics — Attributed to Their Sources

OpenAlex (source S169017477, fetched through the ISSN endpoint in October 2026) records 4,884 works for the title, all of them open access, cited 78,785 times in total, with an h-index of 93 and an i10-index of 2,218. Those are archive figures accumulated over an eighteen-year run and they describe a journal whose most-cited papers — in fractional differential equations especially — were cited very widely indeed. They should not be read as a current performance indicator for the successor title, whose own record begins in 2022. This profile claims no Journal Impact Factor figure for the title: no Journal Citation Reports value was returned by a source consulted for this profile, and the honest course is to leave the field to the attributed OpenAlex record above rather than repeat an unattributed number from an aggregator page. The DOAJ record does supply two practical figures from the journal's SpringerOpen operation: an average publication time of about thirteen weeks, and preservation of the archive through CLOCKSS, LOCKSS and Portico, alongside deposit in the Dutch national library — the arrangements that keep a closed archive permanently reachable after a change of title.

Fees, Licensing and Author Rights

As a fully open access journal, Advances in Difference Equations was funded by article processing charges rather than subscriptions. Its DOAJ record, fetched for this profile in October 2026, lists a maximum charge of USD 1,990 (EUR 1,690; GBP 1,290), with a waiver policy for authors from eligible countries and no other charges; OpenAlex's source record separately records an APC of USD 1,790 in its by-year data for the title's final years — the difference is a reminder that charges changed over the journal's life and between directory snapshots, and that the only authoritative figure for a new submission is the one on the successor journal's own current fees page. Under the journal's SpringerOpen arrangements, articles were published under a Creative Commons Attribution (CC BY) licence and authors retained copyright — the terms recorded in its DOAJ entry — so the whole 2004–2021 archive remains free to read, reuse and build on with attribution, a lasting benefit of the open model the journal adopted at its launch in 2004, when fully open access mathematics journals were still rare.

How Submission Works Now

Authors with a new manuscript in this field should direct it to the successor title, Advances in Continuous and Discrete Models, through Springer's submission system for that journal, following its current author instructions: the successor's scope is broader than the old title's, spanning applied mathematics and data sciences, so the fit check should be made against the successor's stated sections rather than against the archive of the old journal. Authors citing or building on the archive should cite articles under the title and year in which they appeared — Advances in Difference Equations up to volume 2021 — using the article's DOI, which remains live. Readers who find a citation to the old title in a recent reference list are looking at a citation to the archive, not an error: with close to five thousand articles in print, the archive will be cited for decades, and its DOIs and ISSNs are the keys that resolve those citations correctly.

Neighbouring Journals

Readers of this archive commonly work with a small family of neighbouring titles. The Journal of Dynamics and Differential Equations (print ISSN 1040-7294, electronic ISSN 1572-9222), published by Springer, covers dynamical systems and differential equations with a theoretical emphasis. Journal of Difference Equations and Applications serves the same discrete-models community through a subscription-and-hybrid model. Fractional Differential Calculus (ISSN 1847-9677), published by Element in Zagreb, is devoted to the fractional operators that filled many of this journal's pages. Functional Differential Equations, published by Ariel University Press, covers the functional branch of the old title's scope. And the direct continuation of this journal itself is Advances in Continuous and Discrete Models (ISSN 2731-4235), whose own JournalsWorld profile carries its post-2022 record. Checking the ISSN before citing is the standing advice for this whole family, whose titles differ by a word or two while their contents and metrics differ entirely.

Do Not Confuse This Journal With Its Near-Namesakes

One word separates this journal from a completely different publication: Advances in Differential Equations — “Differential” in place of “Difference” — is a separate journal from Khayyam Publishing, carrying ISSN 1079-9389, with its own editors, archive and rankings. Bibliographic searches return the two titles side by side, aggregator pages occasionally blend their figures, and more than one author has cited the wrong one. The check that separates them takes seconds: this journal, Advances in Difference Equations, is the SpringerOpen open access title with ISSNs 1687-1839 and 1687-1847 and DOIs in the 10.1186 family; the Khayyam title is a subscription journal in partial differential equations with none of those markers. A second near-namesake sits on JournalsWorld itself: Advances in Mathematics (ISSN 0001-8708) and the North Macedonian Advances in Mathematics: Scientific Journal (ISSN 1857-8365) are both unrelated to this title beyond the shared word “Advances”, which opens the names of dozens of unrelated journals and book series. In this corner of mathematics publishing, the ISSN is not a formality — it is the only part of a citation that cannot be confused.

Reading the Archive Today

The archive this journal leaves behind has a particular shape worth understanding before it is used as evidence of anything. Because SpringerOpen published continuously, the journal's later volumes are very large, and its citation totals are dominated by a highly cited core in fractional differential equations — the area in which the journal, for a period, was one of the highest-volume open venues in the world. OpenAlex's figures make the shape plain: 4,884 works, 78,785 citations, and an i10-index of 2,218, meaning more than two thousand of its articles have been cited at least ten times. A researcher mining the archive for a specific problem — a boundary value problem for a q-difference equation, an oscillation criterion, a fractional model of a biological system — will usually find several candidate papers, and should read them with the journal's review model in mind: single anonymous peer review, an average of about thirteen weeks from submission to publication per the DOAJ record, and immediate online appearance after acceptance. Those were respectable working arrangements for a community journal of its era, and the archive's heavy onward citation is the community's own verdict on the work it carried. What the archive cannot tell a reader is anything about the successor title's present standards or speed: that judgement must be made on the successor's own pages, from 2022 onward, under its new editors and broadened scope.

One further trace of the journal's early history survives in its records: OpenAlex still lists an early homepage for the title at the Hindawi journal site, from the period before the transfer to Springer that the journal's editorial announcement describes. The sequence — launch in 2004, a first home in the early open access movement, transfer into SpringerOpen, a decade of high-volume publication, and a relaunch under a broader title in 2022 — is a compact history of open access mathematics publishing itself, and it is why this profile treats the title change as a continuation to be explained rather than a disappearance to be reported.

Frequently Asked Questions

What are the ISSNs of Advances in Difference Equations? Print ISSN 1687-1839 and electronic ISSN 1687-1847, the pair stored on this record and confirmed by the journal's DOAJ record and its OpenAlex source record.

Is Advances in Difference Equations still publishing? Under that title, no. It completed its last volume in 2021 and continued from 1 January 2022 as Advances in Continuous and Discrete Models: Theory and Modern Applications, under a new ISSN (2731-4235). The 2004–2021 archive remains fully published and citable.

Who published the journal? SpringerOpen, the open access imprint of Springer Nature, per the journal's DOAJ record; an editorial announcement in the journal records its transfer to Springer to join the SpringerOpen range, with its founding editor-in-chief continuing.

Was the journal open access? Yes — fully open access from 2004, with articles under a CC BY licence, authors retaining copyright, and the archive preserved through CLOCKSS, LOCKSS and Portico, all per its DOAJ record.

What did it cost to publish? The journal's DOAJ record lists a maximum article processing charge of USD 1,990 (EUR 1,690; GBP 1,290) with waivers for eligible countries; OpenAlex records USD 1,790 in its by-year data for the final years. For a new submission, the successor journal's current fees page is authoritative.

What are the journal's citation figures? OpenAlex (source S169017477, checked October 2026) records 4,884 works cited 78,785 times, an h-index of 93 and an i10-index of 2,218, accumulated across the 2004–2021 run under this title.

Where should I submit a new paper on difference equations? To the successor title, Advances in Continuous and Discrete Models, through Springer's current submission route for that journal — new submissions have been considered under the new title since 1 July 2021, per Springer Nature's announcement.