We consider a diusion process (Xt) t≥0 , with drift b(x) and diusion coecient σ(x). At discrete times t k = kδ for k from 1 to M , we observe noisy data of the sample path, Y kδ = X kδ + ε k. The random variables (ε k) are i.i.d, centred and independent of (Xt). The process (Xt) t≥0 is assumed to be strictly stationary, β-mixing and ergodic. In order to reduce the noise eect, we split data into...

In this contribution, a wave equation with time-dependent variable-order fractional damping term and nonlinear source is considered. Avoiding the circumstances of expressing equations via closed-form expressions in terms special functions, we investigate existence uniqueness problem Rothe’s method. First, weak formulation for considered proposed. Then, solution established by employing Grönwall...

In this work, we suggest a novel iterative method to give approximate solutions of nonlinear wave-like equations fractional order with variable coefficients. The advantage the proposed is ability combine two different methods: Shehu transform and homotopy analysis method, in addition providing an solution form convergent series easily computable components, requiring no linearization or small p...

     Salt crystallization is one of the most powerful weathering agents that may cause a rapid change in the mechanical properties of stones, and thus limit their durability. Consequently, determining the mechanical properties of stones due to salt crystallization is important for natural building stones used in marine environmental and mild climatic conditions, which expose excessive salt crys...

Abstract We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter a solution corresponding linear equation. The are small and decay as $|x|\to \infty$ , but allowed be time dependent. proof uses local energy estimates establish of $L^{6}$ norm $t\to .

The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting walks can quite different, however. coefficient made responsible for size jumps or intensity jumps. limit does not feel difference. situation changes if we model jump-type approximations via CTRW with non-exponential waiting times. If make and take times from domain attraction ...

Abstract In this manuscript, we examine both the existence and stability of solutions to implicit boundary value problem Caputo fractional differential equations variable order. We construct an example illustrate validity observed results.