Sentence examples for article we established the from inspiring English sources

In this article, we established the existence and uniqueness of the solution for a generalized class of fractional order differential equations involving the Riemann-Liouville differential operator on unbounded domain [0, +∞). The contraction principle has been used to obtain the results in this article.

In this article, we establish the exact solutions for the combined KdV-mKdV and Gardner-KP equations.

In this article, we establish the new result on homoclinic orbits for a class of damped vibration systems.

In this article, we establish the nonemptiness and boundedness of the solution set for the GVEP under a relatively weaker condition.

For A ∈ C B ( X ) and x ∈ X, we have d ( x, A ) = 0 ⇔ x ∈ Ā = A. In this article, we establish the analogous of Theorem 1.2 on a complete b-metric space.

In this article, we establish the extreme solutions (maximal and minimal solutions) for fractional differential equation with maxima in sense of Riemann-Liouville fractional operators, by using the Tarski's fixed point theorem.

In this article we establish the following Adams type inequality in the hyperbolic space HN:supu∈C∞c HN),∫HN Pku udvg≤1∫HN eβu2−1)dvg<∞ iff β≤β0(N,k) where 2k= N, Pk is the critical GJMS operator in HN and β0(N,k) is as defined in (1.3).

Therefore, in this article, we establish the POD-based reduced-order TSCFE extrapolation iterative format for 2D heat equations and provide the error estimates of the POD-based reduced-order TSCFE solutions and the algorithm implementation of the POD-based reduced-order TSCFE extrapolation iterative format.

In this article, we establish the generalized Hyers-Ulam (or Hyers-Ulam-Rassais) stability of Jordan homomorphisms and Jordan derivations of the following parametric additive functional equation: ∑ i = 1 m f ( x i ) = 1 2 m ∑ i = 1 m f m x i + ∑ j = 1, j ≠ i m x j + f ∑ i = 1 m x i. for a fixed positive integer m with m ≥ 2, on fuzzy Banach algebras.

However, in a previous article, we established that the diffusion may admit several invariant probabilities, provided that the external force derives from a non-convex potential.

In the present article we established an in vitro model system to investigate the survival and phenotype of human MSCs following injection into bovine NP tissue explants to test the following hypothesis: that the IVD tissue niche itself can induce the differentiation of MSCs to a disc-like phenotype and direct the cells to form a new and appropriate matrix.