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Fractal Fract
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Advances in Boundary Value Problems for Fractional Differential Equations, 4th...
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Advances in Boundary Value Problems for Fractional Differential Equations, 4th Edition

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: 10 November 2026 | Viewed by 1447

Special Issue Editor

Prof. Dr. Rodica Luca

E-Mail Website
Guest Editor
Department of Mathematics, "Gheorghe Asachi" Technical University of Iasi, Blvd. Carol I, nr. 11, 700506 Iasi, Romania
Interests: fractional differential equations; ordinary differential equations; partial differential equations; finite difference equations; boundary value problems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional differential equations are extensively applied in the mathematical modelling of real-world phenomena that occur in scientific and engineering disciplines. This Special Issue will cover recent developments in the theory and applications of fractional differential equations, inclusions, and inequalities, as well as systems of fractional differential equations with Riemann–Liouville, Caputo, and Hadamard derivatives, or other generalized fractional derivatives, subject to various initial and boundary conditions. We welcome contributions pertaining to problems such as the existence, uniqueness, multiplicity, and nonexistence of solutions or positive solutions; the stability of solutions; and numerical computations for these models.

The articles published in the first and second volumes of this Special Issue are listed below:

https://www.mdpi.com/journal/fractalfract/special_issues/BVP_FDE

https://www.mdpi.com/journal/fractalfract/special_issues/BVP_FDE2

The third volume is also available at the following link：

https://www.mdpi.com/journal/fractalfract/special_issues/BVP_FDE3

Prof. Dr. Rodica Luca
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional differential equations
  • fractional differential inclusions
  • fractional differential inequalities
  • initial value problems
  • boundary value problems
  • existence and nonexistence
  • uniqueness and multiplicity
  • stability
  • numerical computations

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Further information on MDPI's Special Issue policies can be found here.

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Published Papers (3 papers)

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Research

19 pages, 327 KB  
Article
New Results for a Higher-Order Hadamard-Type Fractional Differential Equation with Integral and Discrete Boundary Conditions on an Unbounded Interval
by Haiyan Zhang and Yaohong Li
Fractal Fract. 2026, 10(3), 141; https://doi.org/10.3390/fractalfract10030141 - 25 Feb 2026
Viewed by 277
Abstract
This study concentrates on a higher-order Hadamard fractional differential equation defined on an unbounded interval, which is subject to integral and discrete boundary conditions. Through the employment of the upper and lower solution method combined with Banach’s contraction mapping principle, we have successfully [...] Read more.
This study concentrates on a higher-order Hadamard fractional differential equation defined on an unbounded interval, which is subject to integral and discrete boundary conditions. Through the employment of the upper and lower solution method combined with Banach’s contraction mapping principle, we have successfully established distinct iterative sequences for the targeted differential equation. To demonstrate the practical relevance of our theoretical findings, we provide a typical example. Full article
(This article belongs to the Special Issue Advances in Boundary Value Problems for Fractional Differential Equations, 4th Edition)
26 pages, 421 KB  
Article
Normalized Solutions and Critical Growth in Fractional Nonlinear Schrödinger Equations with Potential
by Jie Xu, Qiongfen Zhang and Xingwen Chen
Fractal Fract. 2026, 10(2), 85; https://doi.org/10.3390/fractalfract10020085 - 26 Jan 2026
Viewed by 608
Abstract
We investigate the existence of positive normalized (mass-constrained) solutions for the fractional nonlinear Schrödinger equation [...] Read more.
We investigate the existence of positive normalized (mass-constrained) solutions for the fractional nonlinear Schrödinger equation (−Δ)sv+V(x)v=λv+μ|v|p−2v+|v|2s*−2vinRN,∥v∥22=b2, where N>2s, s∈(0,1), μ>0, p∈(2,2s*), and 2s*=2NN−2s. Here, λ∈R denotes the Lagrange multiplier associated with the prescribed mass b>0. The potential V∈C1(RN) is allowed to be nonconstant and satisfies V(x)→V∞ as |x|→∞; moreover, the perturbations induced by V−V∞ and x·∇V are assumed to be small in the quadratic-form sense compared with the fractional Dirichlet form ∥(−Δ)s/2v∥22. Using the Caffarelli–Silvestre extension, we establish a Pohozaev identity adapted to the presence of V(x) and introduce a Pohozaev manifold on the L2-sphere. Combining Jeanjean’s augmented functional approach with a splitting analysis at the Sobolev-critical level, we construct compact Palais–Smale sequences below a suitable critical energy level. As a consequence, we prove the existence of positive normalized solutions for small masses b∈(0,b0) in the L2-critical and L2-supercritical regimes (with respect to the lower-order power p). Full article
(This article belongs to the Special Issue Advances in Boundary Value Problems for Fractional Differential Equations, 4th Edition)
24 pages, 359 KB  
Article
Existence Results for a Coupled System of Nabla Fractional Equations with Summation Boundary Conditions
by Nikolay D. Dimitrov and Jagan Mohan Jonnalagadda
Fractal Fract. 2026, 10(2), 76; https://doi.org/10.3390/fractalfract10020076 - 23 Jan 2026
Viewed by 308
Abstract
The aim of the current manuscript is to study a coupled system of nabla fractional equations with general summation boundary conditions depending on parameters. We deduce the expression of the Green’s function and we obtain useful bounds of it. Using these bounds, under [...] Read more.
The aim of the current manuscript is to study a coupled system of nabla fractional equations with general summation boundary conditions depending on parameters. We deduce the expression of the Green’s function and we obtain useful bounds of it. Using these bounds, under suitable conditions, we obtain existence results by implying a few classical fixed point theorems. Then, we show that there exists an interval for the parameters, where the Green’s function is strictly positive, and we are able to deduce existence, nonexistence, and multiplicity results for our studied problem using the same theory. At the end of this work, we deliver some numerical examples to clarify our theoretical results. Full article
(This article belongs to the Special Issue Advances in Boundary Value Problems for Fractional Differential Equations, 4th Edition)
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