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Collection: Review Articles

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Quintic and Septic $C^2$-spline methods for initial fractional differential equations: Quintic and septic $C^2$-spline methods

In this paper, we developed Quintic and Septic C2C2-spline methods for solving initial fractional differential equations. The convergence analysis of the methods is discussed. Illustrative examples are included to demonstrate the validity and…

Exponential stabilization of an Euler-Bernoulli beam under boundary control

We study the free vibration of an Euler-Bernoulli beam without internal damping. By applying suitable control at the free boundary, we can exponentially dampen these vibrations. The exponential stability was proven using the Lyapunov method, and the…

Non-polynomial fractional spline method for solving Fredholm integral equations

A new type of non-polynomial fractional spline function for approximating solutions of Fredholm-integral equations has been presented. For this purpose, we used a new idea of fractional continuity conditions by using the Caputo fractional derivative…

Generalized contraction theorem in M -fuzzy cone metric spaces

This work defines MM-Fuzzy Cone Metric Space, as a new metric space. It also analyzes possible forms of contractive conditions and groups them accordingly to set up generalized contractive conditions for self-mappings defined over MM-fuzzy cone…

Effect of dispersal in two-patch environment with Richards growth on population dynamics

In this paper, we consider a two-patch model coupled by migration terms, where each patch follows a Richards law. First, we prove the global stability of the model. Second, in the case when the migration rate tends to infinity, the total carrying…

An approximate solution for the time-fractional diffusion equation

In this paper, a numerical method based on a finite difference scheme is proposed for solving the time-fractional diffusion equation (TFDE). The TFDE is obtained from the standard diffusion equation by replacing the first-order time derivative with…

The adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data: Adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data

In this work, we consider the nonparametric estimation of the probability density function for nonnegative heavy-tailed (HT) data. The objective is first to propose a new estimator that will combine two regions of observations (high and low density).…

Uniqueness and stability of parameter identification in elliptic boundary value problem

This paper concerns the uniqueness and stability of an inverse problemin PDE. Our problem consists of identifying two parameters b(x)b(x) and c(x)c(x) in the following boundary-value…

On a viscoelastic plate equation with a polynomial source term and p(x,t)-Laplacian operator in the presence of delay term

In this paper, the blow-up of solutions for a Dirichlet-Neumann problem to initial nonlinear viscoelastic plate equation with a lower order perturbation of p(x,t)-Laplacian operator in the presence of time delay is obtained. Under suitable conditions…

Probability tail for linearly negative quadrant dependent random variables of partial sums and application to linear model: Inequalities for LNQD R.V of partial sums and application

In this paper, we establish a new concentration inequality and complete convergence of weighted sums for arrays of rowwise linearly negative quadrant dependent (LNQD, in short) random variables and obtain a result dealing with complete convergence of…

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