To obtain approximate-exact solutions to nonlocal initial-boundary value problems (IBVPs) of linear and nonlinear parabolic hyperbolic partial differential equations (PDEs) subject initial boundary conditions integral type, the homotopy perturbation method (HPM) is utilized in this study. The HPM used solve specified IBVPs, which are then transformed into local Dirichlet IBVPs. Some examples de...

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial different...

We reduce the two phase Stefan problem with kinetic to a system of nonlinear Volterra integral equations of second kind and apply Newton's method to linearize it. We found product integration solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. Systemtheoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a sing...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

<p style='text-indent:20px;'>In this paper, we study the nonlocal problem for pseudo-parabolic equation with time and space fractional derivatives. The derivative is of Caputo type order <inline-formula><tex-math id="M1">\begin{document}$ \sigma,\; \; 0<\sigma<1 $\end{document}</tex-math></inline-formula> id="M2">\begin{document}$ \alpha,\beta &amp...

Hellaby & Dray have recently claimed that matter conservation fails under a change of signature, compounding earlier claims that the standard junction conditions for signature change are unnecessary. In fact, if the field equations are satisfied, then the junction conditions and the conservation equations are satisfied. The failure is rather that the authors did not make sense of the field equa...