This paper is devoted to the study of a coupled system of fractional Langevin equations involving the Psi-Hilfer fractional derivative and nonlocal Riemann-Stieltjes integral boundary conditions. By transforming the problem into an equivalent system of integral equations, sufficient conditions for the existence of solutions are established via Schauder's fixed point theorem and the Leray-Schauder nonlinear alternative. In addition, uniqueness results are obtained by applying the Banach contraction principle. Several illustrative examples are provided to demonstrate the applicability of the theoretical results and to validate the proposed approach.

This study investigates a class of nonlinear ϕ -Hilfer fractional generalized double-phase problems governed by the p-Laplace operator under Dirichlet boundary conditions. More precisely, we establish the existence of nontrivial solutions in the presence of both logarithmic nonlinearities and singular perturbation terms. To do this, we combine the min–max method with variational techniques. We rigorously demonstrate the existence of nontrivial weak solutions to the proposed class of problems. The theoretical results obtained are novel and provide a significant generalization of several existing contributions in the literature. Beyond their theoretical interest, such fractional double-phase mo dels have several applications in various fields of applied mathematics and physics. They can be used to describe heterogeneous materials with nonstandard growth properties, anomalous diffusion processes in viscoelastic media, phase transition phenomena, and nonlinear heat conduction in materials with memory effects. Moreover, the presence of the ϕ -Hilfer fractional operator allows a more accurate modeling of systems exhibiting both local and nonlocal interactions, bridging both the classical and fractional dynamics and the analytical framework.

In this article, we investigate certain subcritical and critical equations involving the fractional -Laplace operator. More precisely, using fibering maps and the Nehari manifold, we establish the multiplicity of solutions for the following problem: where is a smooth bounded domain, is the fractional -Laplacian, and are positive parameters, and are homogeneous functions of degrees and with . Our results are novel and extend previous works by considering more general growth conditions.

This study investigates a class of-Hilfer generalized fractional nonlinear double-phase problems with Dirichlet boundary conditions, focusing on the existence of nonnegative solutions with logarithmic nonlinearity. By using Nehari manifold minimization techniques and variational approaches, we demonstrate the existence of positive solutions dependent on the parameter xi in appropriates-Hilfer fractional spaces. Our findings are novel and contribute to expanding the knowledge base on double-phase problems and-Hilfer generalized fractional differential equations with Dirichlet boundary conditions.

. In this work, we investigate a double-phase problem involving Riemann-Liouville derivative and a p(t)-Laplacian operator. More precisely, we will use a variational method with the critical theorem of Bonanno and Marano to prove the existence of at least three nontrivial solutions for such a problem. An illustrative example is presented at the end of this work to enhance the validity of our main results.

In this paper, we study the existence and the multiplicity of solutions for a fractional problem with variable exponents and singular nonlinearity. More precisely, we use the variational and the Nehari manifold methods to prove the existence of two nontrivial solutions for such a problem which involves a general integro-differential operator of nonlocal fractional type.

This paper investigates multiplicity results for weak solutions to a degenerate weighted elliptic problem involving Leray-Lions operators, a Hardy-type potential, and a nonlocal source term that may exhibit singularities within the domain 𝒟 . More precisely, we establish two main results. In the first, we employ critical point theory to demonstrate the existence of at least two distinct solutions in the superlinear case. In the second, we apply the variational method to prove the existence of three weak solutions in the sublinear case. These findings extend to a broad class of nonlinear problems in mathematical physics, addressing challenges related to degeneracy, Hardy-type singularities, and nonlocal interactions.

Motivated by some recent results concerning the stability of second-order systems of nonlinear difference equations, we aim in this paper to investigate the global asymptotic stability of a third-order twodimensional system. Furthermore, we discuss the convergence of solutions of this system. Moreover, we establish two asymptotic relations for solutions. Finally, many illustrative examples are given

In this work, we investigate the existence of weak solutions for a new class of fractional differential equations containing a singular term and the generalized φ-Hilfer fractional derivative with variable exponent nonlinearities. Such problems arise naturally in several applied fields, including electrorheological fluids, image processing, elasticity, and models exhibiting Lavrentiev-type phenomena, where variable exponent structures play a crucial role. The studied problem is further complicated by the presence of singular terms, which pose analytical challenges due to their behavior near the origin. To address this difficulty, we employ advanced variational techniques, particularly the Min–Max method analyzed in the framework of variable exponent Sobolev spaces, which allow us to treat nonstandard growth and spatial heterogeneity. By carefully constructing an appropriate energy functional and verifying the necessary compactness and coercivity conditions, we establish the existence of a nontrivial weak solution. The use of the Min–Max method is justified by the geometry of the associated functional, and critical point theory is employed to overcome difficulties caused by the lack of smoothness and the singular behavior of the nonlinearities. Moreover, we provide explicit examples of admissible nonlinearities illustrating the applicability of our main theorem. Our results extend and generalize several previous works by incorporating both the φ-Hilfer derivative an operator unifying many classical and modern fractional derivatives and the flexibility of variable exponent analysis. This paper contributes to the theory of fractional variational problems and offers potential applications in modeling physical systems with spatially variable features and memory effects.

In this work, we studied the multiplicity of solutions for a Kirchhoff problem involving the $ \kappa(\xi) $-fractional derivative and critical exponent. More precisely, we transformed the studied problem into an integral equation that lead to the study of the critical point for the energy functional; after that, we presented and proved some properties related to this functional and demonstrated that the energy functional satisfied the geometry of the mountain pass geometry. Finally, by applying the mountain pass theorem for the even functional, we proved that this functional admitted infinitely many critical points, which means that the studied problem has infinitely many solutions.

In this paper, we consider a class of Steklov p(x)-Laplacian problems with a critical exponent, given by the following equation: { (-triangle)(p(x))u = |u|(r(x)-2)u + f (x, u), in Omega, |del u|(p(x)-2) partial derivative u/partial derivative v = |u|(s(x)-2)u, on partial derivative O, where Omega subset of R-N(N >= 2) is a bounded domain with Lipschitz boundary partial derivative Omega. Here, partial derivative/partial derivative v denotes the outer unit normal derivative, the function f : Omega x R -> R is a Caratheodory function satisfying appropriate assumptions, and the functions p and r are continuous in Omega, such that 1 < r(x) <= p(& lowast;)(x) for all x is an element of Omega, where p(& lowast;)(x) represents the critical Sobolev exponent. To establish the existence and multiplicity of solutions, we employ variational methods, including the mountain pass theorem and symmetric mountain pass theorem, combined with the concentration-compactness principle. These techniques enable us to find solutions that satisfy the given boundary conditions and exhibit interesting properties related to the critical exponent.

This paper is dedicated to the analytical investigation of the global dynamics of an SEIR epidemiological model that incorporates latency age (the time spent by an individual in the exposed class before becoming infectious) and a general nonlinear incidence rate. In this model, to reflect the dependence of disease progress on the latency age, the exposed class is structured by the latency age, and the rate at which the latent individual becomes infected, and the removal rate are assumed to depend on the latency age. By analyzing the characteristic equations associated with each equilibrium, we study the local stability of both the disease-free and endemic steady states of the model. Moreover, it is proven that the semiflow generated by this system is asymptotically smooth, and if the basic reproduction number is greater than unity, the system is uniformly persistent. Furthermore, based on Lyapunov functional and LaSalle’s invariance principle, the global dynamics of the model are established. It is obtained that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable and hence the disease dies out; however, if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable, and the disease persists. Numerical simulations are carried out to illustrate the main analytic results.

This work examines a singular elliptic problem with a fractional and a non-local integrodifferential operator. The question of whether solutions exist is transformed into the existence of critical points of the associated functional energy, to be more specific. The existence of a critical point is then demonstrated by combining the variational method with some monotonicity arguments. After this, due to the singular non-linearity, we manually demonstrate that this critical point is a weak solution for such a problem.

We study a nonlinear eigenvalue problem governed by the psi -Hilfer fractional derivative, arising in the context of capillarity theory with Dirichlet boundary constraints. The nonlinearity involved generally fails to meet Ambrosetti-Rabinowitz-type growth conditions. To address this, we develop a framework that combines pseudomonotone operator theory with variational methods in fractional psi-Hilfer Sobolev spaces, proving the existence of weak solutions.

This study examines the existence of a solution for a nonvariational Langevin equation that involves the $ \psi $-Hilfer fractional derivative. More specifically, we apply the mountain pass theorem, and then an iterative approach to establish the existence of a solution for the problem.

In this paper, we use the variational method to study some Steklov problems involving the $p(x)$-$q(x)$-Laplace operator. Specifically, in the first part of this paper, we combine the mountain pass theorem with Ekeland's variational principle to prove the existence of two nontrivial weak solutions. Furthermore, in the second part of this work, we use the symmetric version of the mountain pass theorem to prove the existence of an infinite number of solutions to such problems.

In the present paper, we will study the multiplicity of solutions for some classes of boundary value problems involving the Riemann Liouville operators and the p-Laplacian operator. The proofs are based on the variational method combined with the Nehari manifold method and the fibering map analysis.

In this paper, we investigate a perturbed parabolic problem involving the Laplace–Beltrami operator on a smooth compact Riemannian manifold M. For a strongly local Dirichlet form in L2(M). More precisely, we begin by proving that, in the case of the existence of a non-negative solution, the potential can be written as a derivative of some functions which are locally integrable on M; after that, we prove the existence of a non-negative solution for such problems.

This paper dealt with the existence of multiple solutions for some singular p(s)-Laplacian problems involving the phi-Hilfer derivative. Precisely, we combined the variational method with the Nehari manifold to prove that such a problem admited two nontrivial solutions. An example was presented to illustrate the effectiveness of our main result.