In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has general discontinuous kernel based on position time space. Conditions of the existence uniqueness solution provided through principal form integral equation, Banach fixed point theorem. After applying properties integral, Fr-NMIDE conformed to Volterra–Hammerstein (V-HIE) second kind, with ...

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...

Some New Uniqueness Results of Solutions for Fractional Volterra-Fredholm Integro-Differential Equations

Abstract. In this study we developed and modified Taylor expansion method for approximating the solution of linear Fredholm and Volterra integro-differential equations. Via Taylor’s expansion of the unknown function at an arbitrary point, the integro-differential equations to be solved is approximately transformed into a system of linear equations for the unknown and its derivatives which can b...

The purpose of this paper is to investigate some qualitative properties solutions nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo derivatives. These include uniform stability, asymptotic Mittag–Leffer stability and boundedness. presented results are proved by defining an appropriate Lyapunov function applying the Lyapunov–Razumikhin method (LRM). Henc...

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations.  2003 Elsevier Science (USA). All rights reserved.

Abstract Analytical description of vibration loads the complex construction structure is considered as a system masses connected by means viscoelastic springs. To take into account rheological properties spring material, Boltzmann-Volterra principle used. A mathematical model problem under consideration has been developed, which boils down to solution nonlinear integro-differential equations. m...