In this paper, we focus on a generalized singular fractional order Kelvin-Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin-Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results.
In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball. Under some suitable local growth conditions for nonlinearity, several new results are obtained by using the fixed-point theorem.
In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder's fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.
In this paper, we study a class of singular fractional order differential system with a changing-sign perturbation which arises from fluid dynamics, biological models, electrical networks with uncertain physical parameters and parametrical variations in time. Under suitable growth condition, the singular changingsign system is transformed to an approximately singular fractional order differential system with positive nonlinear term, then the existence of positive solution is established by using the known fixed point theorem.
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