Fractional Calculus and Applied Analysis

Top Research Topics at Fractional Calculus and Applied Analysis?

Fractional Calculus and Applied Analysis focuses largely on the fields of Mathematical analysis, Fractional calculus, Applied mathematics, Pure mathematics and Fractional differential. The journal explores topics in Mathematical analysis which can be helpful for research in disciplines like Type (model theory) and Nonlinear system. Fractional Calculus and Applied Analysis emphasizes research on Fractional calculus, which includes concerns such as Mittag-Leffler function.

While Applied mathematics is the focus of Fractional Calculus and Applied Analysis, it also provided insights into the studies of Order (group theory) and Stability (probability).

• Mathematical analysis (41.24%)
• Fractional calculus (36.98%)
• Applied mathematics (26.96%)

What are the most cited papers published in the journal?

• Ten equivalent definitions of the fractional laplace operator (293 citations)
• Discrete-time fractional-order controllers (219 citations)
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation (209 citations)

Research areas of the most cited articles at Fractional Calculus and Applied Analysis:

The published articles are organized to address concerns in the fields of Fractional calculus, Mathematical analysis, Applied mathematics, Calculus and Boundary value problem. Pure mathematics, Derivative, Type (model theory), Differential equation and Integral equation are some topics wherein Fractional calculus research discussed in the most cited publications has an impact. While the most cited articles focused on Mathematical analysis, they were also able to explore topics like Diffusion equation and Nonlinear system.

What topics the last edition of the journal is best known for?

• Mathematical analysis
• Algebra
• Real number

The previous edition focused in particular on these issues:

The journal covers a variety of subjects, including Applied mathematics, Fractional calculus, Mathematical analysis, Pure mathematics and Type (model theory). In it, Stability (probability), Boundary value problem, Sturm–Liouville theory and Differential equation are investigated in conjunction with one another to address concerns in Applied mathematics research. Topics in Fractional calculus were tackled in line with various other fields like Singular perturbation, Order (ring theory), Renormalization group, Mathematical physics and Operational calculus.

Fractional Calculus and Applied Analysis connects the study in Mathematical analysis with the closely related area of Nonlinear system. The journal explores issues in Pure mathematics which can be linked to other research areas like Function (mathematics) and Reaction–diffusion system. While Type (model theory) is the focus of it, it also provided insights into the studies of Uniqueness, Multinomial distribution, Monotone polygon and White noise.

The most cited articles from the last journal are:

• Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations (9 citations)
• Operational calculus for the general fractional derivative and its applications (8 citations)
• An efficient localized collocation solver for anomalous diffusion on surfaces (4 citations)

Papers citation over time

A key indicator for each journal is its effectiveness in reaching other researchers with the papers published at that venue.

The chart below presents the interquartile range (first quartile 25%, median 50% and third quartile 75%) of the number of citations of articles over time.

Top authors and change over time

The top authors publishing in Fractional Calculus and Applied Analysis (based on the number of publications) are:

• Virginia Kiryakova (59 papers) published 4 papers at the last edition, 2 less than at the previous edition,
• YangQuan Chen (21 papers) published 2 papers at the last edition the same number as at the previous edition,
• Francesco Mainardi (15 papers) published 1 paper at the last edition the same number as at the previous edition,
• J. A. Tenreiro Machado (15 papers) published 2 papers at the last edition,
• Yuri Luchko (14 papers) published 2 papers at the last edition the same number as at the previous edition.

The overall trend for top authors publishing in this journal is outlined below. The chart shows the number of publications at each edition of the journal for top authors.

Top affiliations and change over time

Only papers with recognized affiliations are considered

The top affiliations publishing in Fractional Calculus and Applied Analysis (based on the number of publications) are:

• Bulgarian Academy of Sciences (40 papers) published 5 papers at the last edition, 2 less than at the previous edition,
• King Abdulaziz University (18 papers) absent at the last edition,
• University of Novi Sad (15 papers) absent at the last edition,
• Hohai University (13 papers) published 1 paper at the last edition,
• University of Bologna (12 papers) published 1 paper at the last edition the same number as at the previous edition.

The overall trend for top affiliations publishing in this journal is outlined below. The chart shows the number of publications at each edition of the journal for top affiliations.

Publication chance based on affiliation

The publication chance index shows the ratio of articles published by the best research institutions in the journal edition to all articles published within that journal. The best research institutions were selected based on the largest number of articles published during all editions of the journal.

The chart below presents the percentage ratio of articles from top institutions (based on their ranking of total papers).Top affiliations were grouped by their rank into the following tiers: top 1-10, top 11-20, top 21-50, and top 51+. Only articles with a recognized affiliation are considered.

During the most recent 2021 edition, 5.45% of publications had an unrecognized affiliation. Out of the publications with recognized affiliations, 21.15% were posted by at least one author from the top 10 institutions publishing in the journal. Another 9.62% included authors affiliated with research institutions from the top 11-20 affiliations. Institutions from the 21-50 range included 19.23% of all publications and 50.00% were from other institutions.

Returning Authors Index

A very common phenomenon observed among researchers publishing scientific articles is the intentional selection of journals they have already attended in the past. In particular, it is worth analyzing the case when the authors participate in the same journal from year to year.

The Returning Authors Index presented below illustrates the ratio of authors who participated in both a given as well as the previous edition of the journal in relation to all participants in a given year.

Returning Institution Index

The graph below shows the Returning Institution Index, illustrating the ratio of institutions that participated in both a given and the previous edition of the conference in relation to all affiliations present in a given year.

The experience to innovation index

Our experience to innovation index was created to show a cross-section of the experience level of authors publishing in a journal. The index includes the authors publishing at the last edition of a journal, grouped by total number of publications throughout their academic career (P) and the total number of citations of these publications ever received (C).

The group intervals were selected empirically to best show the diversity of the authors' experiences, their labels were selected as a convenience, not as judgment. The authors were divided into the following groups:

• Novice - P < 5 or C < 25 (the number of publications less than 5 or the number of citations less than 25),
• Competent - P < 10 or C < 100 (the number of publications less than 10 or the number of citations less than 100),
• Experienced - P < 25 or C < 625 (the number of publications less than 25 or the number of citations less than 625),
• Master - P < 50 or C < 2500 (the number of publications less than 50 or the number of citations less than 2500),
• Star - P ≥ 50 and C ≥ 2500 (both the number of publications greater than 50 and the number of citations greater than 2500).

The chart below illustrates experience levels of first authors in cases of publications with multiple authors.