This work deals with a class of double phase problems with variable exponents of Kirchhoff-Schr & ouml;dinger type within the framework of Musielak-Orlicz-Sobolev spaces. By imposing certain assumptions and using the topological degree for a class of ( S + ) {(S_{+})} -demicontinuous operators, we derive the existence of at least one solution for the above problems. Our results are also applicable to problems with no-flux boundary conditions, and extend and generalize many previously published results.

In this work, we investigate the existence of renormalized solutions for a nonlinear parabolic problem with variable exponents and general measure data. The solutions are achieved by combining monotone operator thbory, Marcinkiewicz estimation, and the truncation method.

This work is devoted to the analysis of fuzzy fractional delay differential equations (FDDEs) governed by the generalized Caputo fractional derivative (GCFD). By combining stepwise approximation methods with suitable Gronwall-type inequalities, we establish the existence and uniqueness of solutions. Furthermore, we derive explicit criteria that guarantee the finite-time stability. The theoretical contributions are illustrated with numerical simulations, confirm the analytical findings and demonstrate the effectiveness of the proposed framework in capturing the dynamical behavior of fuzzy fractional delay models.

In this article, we present a novel characterization of the continuity of linear maps within Colombeau algebras. Additionally, we introduce an alternative representation for the contraction of these maps. Moreover, we put forth a new concept of fixed-point theorems in Colombeau algebra, extending classical fixedpoint theorems, including those of Banach, Chatterjea, and Kannan. To underscore the practical relevance of our findings, we offer various examples and applications.

This paper establishes rigorous mathematical foundations for fuzzy fractional delay integrodifferential equations (FFDIDEs) involving the generalized Hukuhara psi-Caputo fractional derivative-a previously unexplored combination in the literature. We address the critical theoretical gap in analyzing systems that simultaneously incorporate fuzzy uncertainty, memory effects (time delays), and non-local dynamics (integral terms). Through an innovative synthesis of Banach's fixed point theorem and a novel monotone iterative technique, we prove: (1) existence and uniqueness of solutions under Lipschitz conditions (Theorems 2 and 3), (2) constructive approximation via monotone sequences converging uniformly to the solution (Lemma 2), and (3) continuous dependence on initial conditions with explicit stability bounds (Theorem 4). Our framework systematically handles both d-increasing and d-decreasing solution cases through a unified psi-Caputo operational calculus. The theoretical advances are validated through computational experiments demonstrating O(h1+alpha) convergence rates for alpha is an element of (0, 1), with MAT-LAB simulations providing quantitative analysis of triangular fuzzy solutions (Example 1, Figures 1-6). Beyond its theoretical contributions, this work enables new applications in fuzzy control systems with delays, fractional-order neural networks with uncertainty, and other complex systems requiring simultaneous treatment of non-locality and vagueness. The results fundamentally extend the existing fuzzy fractional calculus literature by establishing the first comprehensive solution theory for this important class of equations.

The goal of this paper is to investigate the existence and multiplicity of solutions for some p(x)-Laplacian-like problems on Riemannian manifolds with nonlocal terms. Our results are obtained by using the Mountain Pass Theorem and Fountain Theorem.

In this paper, we establish existence results for a class of Choquard-Kirchhoff problems driven by double-phase operators with gradient-dependent exponents. Particular attention is devoted to the analysis of the associated nonlinear differential operator, where we investigate key structural properties such as boundedness, continuity, strict monotonicity, and the (S+)-property condition. These properties play a fundamental role in the construction of an appropriate functional framework and allow the application of the Berkovits topological degree theory. As a consequence, we obtain the existence of weak solutions to the considered problem.

We consider a class of nonlinear parabolic initial boundary value prob- lems having the fractional p(z)-Laplacian operator. By combining variable expo- nent fractional Sobolev spaces with topological degree theory, we establish the existence of a time-periodic non-trivial weak solution.

In the current work, we examine a novel type of fuzzy fractional multipantograph differential equations involving ψ-Caputo derivative. Firstly, we establish the existence result by using Schaefer fixed point theorem and then the uniqueness is proved by using Banach fixed point theorem. Secondly, with aid of generalized Gr¨onwall inequality, we investigative the Ulam–Hyers–Mittag-Leffler stability of solution for the problem under consideration. Lately, two examples are provided to illustrate the theoretical results.

This article is devoted to establishing the existence and uniqueness of solutions to the fractional problem of diffusion waves in the following Colombeau algebra: { D(t)(alpha)u(x, t) + triangle(x)u(x, t) = f (t, u(t, x)); (x, t) is an element of ohm x [0, T] u(0,x) =psi(0)(x) = delta(x); partial derivative(t)u(0, x) = psi 1(x). Where D-t(alpha) is the fractionnal derivative with 1 < alpha < 2, triangle is the Laplace operator, psi(0), psi(1) are generalized functions, delta is distributions and ohm subset of R-n. This study is based on the integral solution of this problem using the Gronwall's lemma. Finally we study the association concept with the classical solution.

This paper employs Colomb eau algebra as a mathematical framework to establish both the existence and uniqueness of solutions for the fractional Schrodinger equation when subjected to singular potentials. A noteworthy contribution lies in the introduction of the concept of a generalized conformable semigroup, marking the first instance of its application. This innovative approach plays a pivotal role in demonstrating the sought-after results within the context of the fractional Schrodinger equation. The utilization of Colomb eau algebra, coupled with the introduction of the generalized conformable semigroup, represents a novel and effective strategy for addressing challenges posed by singular potentials in the study of this particular type of Schrodinger equation.

In this paper, the nonlocal Cauchy problem is discussed for the fuzzy fractional evolution equations in an arbitrary Banach space for order q ∈ (1, 2) and the criteria on the existence and uniqueness of mild fuzzy solutions are obtained by using Schauder’s fixed point theorem. An example to illustrate the applications of main results is also given.

In this paper, we are interested in the existence of weak solutions for a class of Kirchhoff-type systems driven by the(alpha(1)(m); alpha(2)(m))-Kirchhoff-Laplacian operator with the Dirichlet boundary conditions as follows: {-R-1( integral(D) L(psi)(alpha 1)dm) (Delta(alpha 1)(m)psi -|psi|(alpha 1(m)-2)psi ) +delta(1)|psi|(p(m)-2) psi = lambda(1)f(m; psi;del psi) in D; -R-2( integral(D)L(psi)(alpha 2)dm) ( Delta(alpha 2)(m)psi -|psi|(alpha 2(m)-2)psi ) +delta(2)|psi|(q(m)-2) psi=lambda(2)f(m; psi;del psi) in D; y= phi=0 on partial derivative D, where L-psi(alpha 1) and (alpha 2)(psi) are non-local integro-differential operators, Dis an open bounded subset of R-N with the Lipshcitz boundary partial derivative D. Under some suitable assumptions on the functions R-1,R-2,fandg, together with the Berkovits topological degree and the variable exponent Sobolev spaces theory, wediscuss the existence of weak solutions for the above problem on the spaces W-0(1,alpha 1(m))(D) x W-0(1,alpha 2(m))(D).

In this paper, we present some results concerning the existence and multiplicity of solutions for a class of p(x)-Laplacian-like problems with Robin boundary conditions. Specifically, we establish the existence of three solutions in the generalized Sobolev space.

In this manuscript, we look into the existence of solutions to a class of uncertain differential equations with non-local derivatives. The method relies on the Krasnosel’skii fixed point theorem as well as a lengthened Schauder fixed point theorem that is applicable on fuzzy metric spaces. This theorems implies that the topic in question has a fuzzy solution specified on a certain interval. Our strategy requires considering a linked integral problem wherein the aforementioned tools apply. We’ll wrap off with a physical incentive.

On a compact Riemannian manifold without boundary, this work deals with a non-local Kirchhoff-type double phase problem with variable exponents and without the Ambrosetti-Rabinowitz. The first objective of this work is to establish the existence of least energy solutions by using the Mountain Pass Theorem and the restriction of Nehari manifold. Furthermore, the second objective is to establish the existence of an infinite number of small and large energy solutions. To obtain these multiplicity results, respectively the Fountain Theorem and the Dual Fountain Theorem are used.

This manuscript aims to highlight the existence result for a class of nonlinear fuzzy hybrid $ \psi $-Hilfer fractional differential equations. Our approach is based on the application of an extended $ \psi $-Hilfer fractional derivative of order q, σ ∈ (0, 1) valid on fuzzy functions paired with Dhage fixed point theorem. As an example of application, we provide one at the end of this paper to show how the results can be used.

The aim of this paper is to investigate an intuitionistic fuzzy matrix equations. The existence conditions of an intuitionistic fuzzy solution are given and also a method for computing the solution is derived. Finally, some examples are presented to illustrate the effectiveness of the presented method.