Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...

In this paper, two collocation methods based on the shifted Legendre polynomials are proposed for solving system of nonlinear Fredholm-Volterra integro-differential equations. The equation considered in paper involves derivative unknown functions integral term, which makes its numerical solution more complicated. We first introduce a single-step method interval [0, 1]. Next, multi-step version ...

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful al...

Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it therefore further explored this paper. In manuscript, we utilize functionals combined with Laplace transform to qualitatively analyze solutions of equation addition, extend our method nonlinear equations infinite delay, several kernels. We menti...

We survey continuous and discrete regularization methods for first-kind Volterra problems with continuous kernels. Classical regularization methods tend to destroy the non-anticipatory (or causal) nature of the original Volterra problem because such methods typically rely on computation of the Volterra adjoint operator, an anticipatory operator. In this survey we pay special attention to partic...

We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the operator's banded sparsity structure when acting specific Jacobi polynomial bases. The is not restricted to convolution-type kernels of form $K(x,y)=K(x-y)$ but instead works general at competitive speeds and with exponential convergence. provide various numerical experiments problems or witho...