In this paper, we prove a theorem on the existence of solutions for a second
order differential inclusion governed by the Clarke subdifferential of a
Lipschitzian function and by a mixed semicontinuous perturbation.
In this paper, we study the existence of solutions for a system of quadratic
integral equations of Chandrasekhar type by applying fixed point theorem of
a 2 x 2 block operator matrix defined on a nonempty bounded closed convex
subsets of Banach algebras where the entries are nonlinear operators.
AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.
This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.
The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ>0,1≤k≤n−1.
Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients