Applied Mathematics and Nonlinear Sciences

About Applied Mathematics and Nonlinear Sciences

Applied Mathematics and Nonlinear Sciences — Journal Profile

Applied Mathematics and Nonlinear Sciences (AMNS) is an open access journal of applied mathematics and nonlinear science, published on the Sciendo platform by Walter de Gruyter and identified by ISSN 2444-8656. It published its first volume in 2016, founded and led by Editor-in-Chief Juan Luis García Guirao, a full professor of applied mathematics at the Technical University of Cartagena in Spain. Every article carries the journal's ISSN and a DOI, is published open access — articles from its Sciendo archive state a Creative Commons Attribution licence — and is charged, on acceptance, an article processing charge that the publisher's own APC document for this journal sets at USD 2,500. The journal began as a twice-yearly title publishing a few hundred pages a year of densely mathematical work; it has since grown into a very high-volume publication, a transformation that is central to understanding it today and one this profile describes frankly, because authors choosing AMNS in the mid-2020s are choosing the journal as it now is, not only as it was founded. Its scope, in its own framing, is the application of mathematics and nonlinear science across the sciences and engineering — dynamical systems, fractional calculus, fractals, mathematical modelling and computational methods applied to physical, biological, engineering and social problems.

Scope: Applied Mathematics Meets Nonlinear Science

The journal's title states its territory precisely. On the applied mathematics side, it publishes work on differential equations, fractional calculus and fractional differential equations, numerical methods, mathematical modelling, optimization, and the analytic and computational study of equations arising from applications. On the nonlinear sciences side, it publishes work on dynamical systems, chaos and bifurcation, fractal structures and fractal dimension, synchronization, and the behaviour of complex nonlinear systems. The early volumes show this scope in concrete form. The inaugural volume carried a survey treatment of applied mathematics and nonlinear sciences in the war on cancer, written by an international group of mathematical oncology researchers; a study of the perturbed restricted three-body problem by Abouelmagd and Guirao; work on jittering regimes of two spiking oscillators with delayed coupling from researchers at the Institute of Applied Physics of the Russian Academy of Sciences; a survey on fractal dimension for fractal structures; and a homotopy analysis treatment of the lubrication of a long porous slider. Celestial mechanics, neuroscience-adjacent oscillator theory, fractal geometry, fluid lubrication and mathematical medicine in a single volume is the journal's founding character in miniature: the unifying test is not a single application area but whether nonlinear or applied mathematical structure does real work in the paper.

As the journal has grown, its published contents have broadened well beyond that founding core. Its later volumes contain large numbers of papers applying mathematical and computational modelling — including statistical modelling, intelligent algorithms and data-driven methods — to engineering, management, education, economics and other applied settings, alongside continuing work in fractional calculus, dynamical systems and nonlinear equations. Authors should understand the consequence: the journal's name and founding scope describe a mathematical journal, and reviewers and readers formed by that tradition will expect a genuine mathematical or modelling contribution — a model formulated and analysed, an equation solved or characterised, a method developed and tested — rather than a purely descriptive applied study with mathematics mentioned only in passing. The most-cited papers in the journal's record, as summarised by secondary research profiles, remain of the founding type: exact solutions of systems of complex nonlinear models, quantum differential equations, invariant subspace methods for partial differential equations with fractional derivatives, and fractional calculus studies, several of them cited fifty to seventy times. That citation record is a useful guide to what the journal's readership actually uses and cites.

History: From Twice-Yearly Specialist Title to High-Volume Journal

AMNS was launched in 2016, with its first issue carrying submissions received in late 2015 and its articles handled, as the early papers record, through communicating editors with Juan L. G. Guirao's name recurring across the volume — consistent with his role as founding Editor-in-Chief, a role also stated in his published biographies, which note that he became, in 2011, Spain's youngest full professor of mathematics and has published extensively in applied mathematics. The journal's original web home was the UP4Sciences journals site, reflected in the publisher's documents, which still give the editorial office contact at that domain, and its DOIs in the earliest volumes used the 10.21042 prefix before the journal's Sciendo-era DOIs under the 10.2478 prefix. Publication was twice yearly, and the volumes were substantial but recognisably those of a specialist journal: Volume 1 ran to two issues, and as late as Volume 8 (2023) the journal was publishing numbered issues in the same series.

The change since then is one of scale. Secondary journal profiles report that the journal published on the order of 983 articles in 2025 alone — a volume of output many times larger than its founding rhythm, and one that places it among the high-volume open access journals of its field. Scale changes what a journal is, and honest guidance must say so. A high-volume model can offer speed and a home for applied modelling work that specialist titles decline on scope, but it also means an author should verify, at the moment of submission, the things that can change with scale: current indexing status in Scopus and Web of Science, which secondary sources describe inconsistently for this title — SCImago-based reporting has recorded Scopus coverage concentrated in 2020 to 2022, while other profiles describe broader coverage — the current CiteScore or impact metrics, if any are claimed, and the exact current APC and waiver terms in the publisher's live documents. This profile deliberately reports no single impact factor or CiteScore as a settled fact for AMNS, because the figures attributed to it by secondary sources conflict, and presenting a contested number as fact would mislead exactly the authors this profile is meant to help. What is solid, and verified from the publisher's own materials, is the journal's identity, ISSN, publisher, open access model, licence on its archived articles, founding editorship and its USD 2,500 article processing charge.

Publishing Model, Charges and Waivers

AMNS is a fully open access journal: there is no subscription version, and the costs of publication are carried by the article processing charge rather than by readers. The publisher's APC document for the journal states the position in detail that authors should rely on. Each article accepted for publication is subject to an article processing charge of USD 2,500, with fees subject to VAT where applicable. The charge is described as covering the costs of the peer review process, professional typesetting and copyediting, online hosting, long-term preservation, distribution to libraries and content aggregators, and promotion to potential readers. There are no submission charges, so an author risks no fee by submitting and being rejected. Editors and reviewers are not involved in the author payment process and do not discuss charges with authors, and the document states that the ability to pay does not influence whether a manuscript is accepted — payment information is provided only following acceptance.

The same publisher document sets out a waiver policy that authors with limited funding should read before submitting rather than after acceptance. Authors affiliated with an organization listed as an Institutional Member have the APC covered by that membership. Authors working for institutions in developing countries — defined in the document by the World Bank's low-income and lower-middle-income classifications — can apply for a waiver, and other authors who meet neither criterion can also request a waiver or a discount during the submission process. Three practical points follow. First, confirm the current charge in the publisher's live document at submission time, since the archived document used for this profile can be superseded. Second, raise waiver questions during submission, as the document directs, not after an invoice arrives. Third, keep the payment conversation with the editorial office, whose contact the document gives, and not with editors or reviewers, who the publisher explicitly keeps out of the payment process. Articles in the journal's archive are published under a Creative Commons Attribution licence, stated on the article PDFs as the Creative Commons Attribution alone 4.0 licence in earlier volumes, which permits reuse with attribution — the licence authors should expect and should check on their own article at publication.

How to Write for AMNS

• Make the mathematics do the work. Formulate the model, state the equations and assumptions, and analyse or solve them; a paper whose mathematics could be deleted without changing its conclusions is the wrong shape for this journal.
• Anchor in the journal's proven territory. Fractional calculus, dynamical systems, nonlinear equations, fractals, celestial mechanics and mathematical modelling are the areas its most-cited record shows its readers use.
• Use the correct classification codes. Early AMNS papers carry Mathematics Subject Classification and AMS codes; including accurate codes helps the right reviewers and readers find the work.
• Validate computational work. Compare numerical results against analytic solutions, published cases or convergence tests, and report parameters completely enough for repetition.
• Verify indexing before you submit. If your institution requires Scopus or Web of Science coverage, confirm the journal's current status in those databases directly; secondary sources conflict for this title.
• Confirm the APC and any waiver at submission. The publisher's document sets the charge at USD 2,500 with waiver routes; raise membership, country-based or discretionary waivers during submission.
• Check fit against recent issues, not only early ones. The journal's contents have broadened considerably; recent volumes show the applied modelling range it now publishes.

Who the journal suits follows from its history. It suits authors with a genuine applied-mathematical or nonlinear-science contribution — especially in fractional calculus, dynamical systems and mathematical modelling — who want open access publication with a defined charge and a licence that permits wide reuse, and whose institutions have confirmed that the journal's current indexing satisfies their requirements. It is a weaker choice for authors whose primary need is a guaranteed indexing outcome for promotion or graduation until they have verified that outcome themselves, and for authors whose work is applied in topic but not mathematical in method. Reading a recent issue end to end, checking the current publisher documents, and confirming indexing in the databases that matter to you are, for this journal in particular, not optional preliminaries: they are the submission process working as it should.

Frequently Asked Questions

What is the ISSN of Applied Mathematics and Nonlinear Sciences?

ISSN 2444-8656, carried on its articles and matching the record stored on Journals World.

Who publishes Applied Mathematics and Nonlinear Sciences?

The journal is published on the Sciendo platform by Walter de Gruyter; its archived article PDFs state published by Sciendo, and the Journals World record lists De Gruyter.

When was AMNS founded and who edits it?

Its first volume appeared in 2016. Its founding and current Editor-in-Chief is Juan Luis García Guirao of the Technical University of Cartagena, Spain.

Is AMNS open access, and what does it charge?

Yes, it is fully open access, with archived articles under a Creative Commons Attribution licence. The publisher's APC document sets the charge at USD 2,500 per accepted article, with no submission charge and waiver routes described in the same document.

What subjects does AMNS cover?

Applied mathematics and nonlinear science: differential and fractional equations, dynamical systems, chaos and bifurcation, fractals, numerical and computational methods, and mathematical modelling across physical, biological, engineering and social applications.

Does AMNS have an impact factor or CiteScore?

No single figure could be verified consistently from reliable sources during research for this profile — secondary sources conflict, including on the journal's database coverage years — so none is stated as fact here. Verify current metrics and indexing directly in Scopus, Web of Science or the publisher's live pages before relying on them.

How often does AMNS publish?

It began with two issues per year in 2016 and has since grown to very high volume; secondary profiles report roughly 983 articles published in 2025.

Sources and verification: this profile is based on the journal's own archived articles on Sciendo (ISSN, licence, communicating-editor records, subject matter of Volumes 1 and 8), the publisher's article processing charge document for this journal (charge, waiver policy, no submission charge, editorial office contact), published biographical sources for the Editor-in-Chief, and secondary research profiles for citation and volume context, attributed as such. Indexing and metric claims for this title conflict across secondary sources and are therefore reported as unverified rather than asserted.

What Happens After Acceptance: Production and Dissemination

The publisher's own description of what the article processing charge pays for doubles as a map of the journal's production process, and authors can use it to know what to expect. The charge covers the peer review process itself; professional typesetting and copyediting of the accepted manuscript; online hosting of the published article; long-term preservation, which is the publisher's commitment that the article remains accessible as platforms change; distribution to libraries and content aggregators worldwide, which is the channel by which the article reaches readers who never visit the journal's own site; and promotion to potential readers. Two implications follow for authors. First, the accepted manuscript will pass through professional production, so authors should expect copyediting queries and proofs, and should treat the proof stage as the last realistic chance to correct errors in equations, symbols and author details — in a mathematics journal, a mis-set symbol is not a cosmetic fault but a change of meaning, and proofs deserve the same care as the submission itself. Second, because distribution runs through libraries and aggregators as well as the journal site, the metadata an author supplies at submission — title wording, abstract, keywords and subject classification codes — has an outsized effect on whether the right readers ever encounter the paper. A title that names the equation, method or system studied will travel through those channels far better than a general title, and an abstract that states the result, not only the topic, gives aggregators and searchers the material they need. Authors should also confirm, on the published article itself, that the Creative Commons Attribution licence statement appears as expected, since that statement is what legally permits the reuse, translation and text-mining of the work that open access promises.

A Note on Due Diligence for This Journal

Most journal profiles can end with routine advice; this one ends with a specific checklist, because the public record for AMNS contains genuinely conflicting secondary information and the journal has changed greatly in scale since its founding. Before submitting, an author should complete five checks in primary sources. Check the journal's current page on the Sciendo platform for its present editorial board, scope wording and submission route. Check the publisher's current article processing charge document for this journal, since the USD 2,500 figure in this profile comes from the publisher's archived document and charges are revised over time. Check Scopus and the Web of Science Master Journal List directly for the journal's current coverage status under ISSN 2444-8656, rather than relying on any secondary profile — including this one — where reports differ. Check a recent issue, not an early one, to confirm that papers like yours are still being published and to see the present standard of presentation. And check your own institution's rules, because a journal can be legitimate, active and suitable for a paper while still failing a particular institution's list-based requirement. None of these checks takes long, all of them use primary sources, and together they convert the uncertainties honestly recorded in this profile from a risk into a routine. A journal founded in 2016 by a named professor of applied mathematics, published by an established scholarly publisher, with a decade of archived volumes, deserves to be assessed on that verified record — neither inflated by unverified metric claims nor dismissed without evidence — and the checks above are how an author performs that assessment fairly.