‎in this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(vofides‎, ‎for short)‎. ‎in these equations‎, ‎the variable-order fractional integration(vofi) and‎ ‎variable-order fractional derivative (vofd) are described in the‎ ‎riemann-liouville's and caputo's sense,respectively‎. ‎numerical experiments‎, ‎consisting of two exam...

Abstract: In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional or...

In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative order α∈(0,1) for continuous (locally integrable) function u:[0,∞)→E, where E is complex Banach space. our definition, do not require that u(·) continuously differentiable, which enables us to consider wellposedness corresponding relaxation problems in much better theoretical way. More precisely, systema...

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional powerlaw dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We obtain fractional integro-differential equations for electromagnetic waves in a dielectric. The electromagnetic fields in dielectrics demonstrate a fractional ...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

In this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated to verify convergence results and to illustrate the efficiently of the method.

Ahmed A. Hamoud, Nedal M. Mohammed, Homan Emadifar;, Foroud Parvaneh, Faraidum K. Hamasalh, Soubhagya Kumar Sahoo, and Masoumeh Khademi. International Journal of Fuzzy Logic Intelligent Systems 2022;22:391-400. https://doi.org/10.5391/IJFIS.2022.22.4.391

In this article, we consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. In the first part, we deal with two-dimensional integralalgebraic equations. Next, we analyze Volterra integral equations of the first kind with a degenerate matrix-kernel on the diagonal. Finally, the third part of the work is devoted to the analysis of degenerate integro...