Abstract We consider a general class of integro-differential evolution equations which includes the governing equation generalized grey Brownian motion and time- space-fractional heat equation. present relation between parameters distribution underlying stochastic processes, as well discuss different classes processes providing solutions these equations. For subclass equations, containing Maric...

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 ...

The phase difference φ across a Josephson junction is considered for a film with a thickness d λ, where λ is the London penetration depth in the superconducting banks. Special attention is given to the case of a critical current density jc varying along the junction. It is shown that a nonlinear integro-differential equation determines the spatial distribution of φ for d λ. Josephson properties...

Using Banach’s contractive principle and the Laray–Schauder fixed point theorem, we study uniqueness existence of solutions to a nonlinear two-term fractional integro-differential equation with boundary condition based on Babenko’s approach Mittag–Leffler function. The current work also corrects major errors in published paper dealing one-term differential equation. Furthermore, provide example...

In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...