A M\"untz-Collocation spectral method for weakly singular volterra integral equations [PDF]
Journal of Scientific Computing, 2019 In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu ...
Azaiez, Mejdi +3 more
core +5 more sources
Solution of a two-dimensional parabolic model problem in a degenerate angular domain [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In this paper, the boundary value problem of heat conduction in a domain was considered, boundary of which changes with time, as well as there is no the problem solution domain at the initial time, that is, it degenerates into a point.
M.I. Ramazanov +2 more
doaj +2 more sources
Solution of the boundary value problem of heat conduction in a cone [PDF]
Opuscula Mathematica, 2022 In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time.
Murat Ramazanov +2 more
doaj +1 more source
SOLUTION OF A TWO-DIMENSIONAL BOUNDARY VALUE PROBLEM OF HEAT CONDUCTION IN A DEGENERATING DOMAIN
Вестник КазНУ. Серия математика, механика, информатика, 2021 In the paper we consider the boundary value problem of heat conduction outside the cone, i.e. in the domain degenerating into a point at the initial moment of time.
M. I. Ramazanov +1 more
doaj +1 more source
Bounded, asymptotically stable, and L^{1} solutions of Caputo fractional differential equations [PDF]
Opuscula Mathematica, 2015 The existence of bounded solutions, asymptotically stable solutions, and \(L^1\) solutions of a Caputo fractional differential equation has been studied in this paper.
Muhammad N. Islam
doaj +1 more source
Fractal and Fractional, 2023 The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method, the NVFIE
Sahar M. Abusalim +3 more
doaj +1 more source
Computation of semi-analytical solutions of fuzzy nonlinear integral equations
Advances in Difference Equations, 2020 In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A
Zia Ullah +3 more
doaj +1 more source
A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems
Fractal and Fractional, 2023 Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs).
Mohammadhossein Derakhshan +4 more
doaj +1 more source
Generalised Dirichelt-to-Neumann map in time dependent domains [PDF]
, 2012 We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function.
Baratella +11 more
core +1 more source
Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique [PDF]
Computational Algorithms and Numerical DimensionsThis study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented.
Youssef Esmaiel +2 more
doaj +1 more source