Belhireche, Hanane Guebbai, Hamza
Published in
Computational and Applied Mathematics

In this paper, we study the solution existence and uniqueness of a nonlinear Volterra–Fredholm integro-differential equation with weakly singular kernel. The singular part appears in the Volterra integral when we derive the equation. To construct a numerical approximation of the solution we use numerical methods based on the approximation of the in...

Milišić, Vuk Schmeiser, Christian
Published in
Nonlinearity

We consider a nonlinear integro-differential model describing z, the position of the cell center on the real line presented in Grec et al (2018 J. Theor. Biol. 452 35–46). We introduce a new ɛ-scaling and we prove rigorously the asymptotics when ɛ goes to zero. We show that this scaling characterizes the long-time behavior of the solutions of our p...

Dölz, J. Egger, H. Shashkov, V.
Published in
Advances in Computational Mathematics

The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretization, the basic problem can be represented as a matrix-vector product with a lower diagonal but densely populated matrix. For typical applications, like fractional diffusion ...

Parand, K. Hasani, M. Jani, M. Yari, H.
Published in
Computational and Applied Mathematics

In this paper, a new method based on least squares support vector regression (LS-SVR) is presented as a numerical method for solving linear and nonlinear Volterra–Fredholm integral equations. To minimize the residual function associated with the integral equation, the resulting optimization quadratic problem is written as a linear system by introdu...

Abi Jaber, Eduardo

We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is based on approximations using s...

Tunç, Osman
Published in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

In this paper, non-perturbed and perturbed systems of non-linear differential equations with multiple constant delays are considered. Five new theorems on the qualitative properties of solutions, uniform asymptotic stability (UAS) and instability of trivial solution, boundedness and integrability of solutions, are obtained. The technique of the pro...

Sadri, Khadijeh Hosseini, Kamyar Baleanu, Dumitru Ahmadian, Ali Salahshour, Soheil
Published in
Advances in Difference Equations

The shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the num...

Jang, Yongseok Shaw, Simon
Published in
Advances in Computational Mathematics

We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method ...

Nemer, Ahlem Kaboul, Hanane Mokhtari, Zouhir
Published in
Journal of Applied Analysis

In this paper, we consider general cases of linear Volterra integral equations under minimal assumptions on their weakly singular kernels and introduce a new product integration method in which we involve the linear interpolation to get a better approximate solution, figure out its effect and also we provide a convergence proof. Furthermore, we app...

Tunç, Cemil Tunç, Osman
Published in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

In the paper, Tian and Wang (Appl Math Lett 105:106325, 8 pp, 2020, Theorem 1) took into consideration a linear system of integro-delay differential equations (IDDEs) with constant time retardation. In Tian and Wang (2020), the authors proved a new and interesting theorem concerning asymptotically stability of zero solution of that linear system of...