In this paper we aim to construct an abstract model of a differential operator with fractional integro-differential composition in final terms, where modeling is understood as interpretation concrete operators terms the infinitesimal generator corresponding semigroup. We study such Kipriyanov operator, Riesz potential, difference operator. Along this, consider transforms m-accretive generalizat...

In this paper, we prove the existence and uniqueness of a nonlinear perturbed stochastic fractional integro-differential equation of Volterra-Itô type involving nonlocal initial condition by using the theory of admissibility of integral operator and Banach fixed-point principle. Also the stability and boundedness of the second moments of the stochastic solution are studied. In addition, an appl...

The unique solvability in the sense of classical solutions for nonlinear inverse problems to differential equations, solved oldest Dzhrbashyan–Nersesyan fractional derivative, is studied. linear part equation contains a bounded operator, continuous operator that depends on lower-order derivatives, and an unknown element. problem given by equation, special initial value conditions lower overdete...

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

A homogeneous fractional-differential equation with a fractional Hardy—Titchmarsh integral and an unbounded operator coefficient in Banach space is considered. The conditions for the representation of solution form Danford—Cauchy are established, exponentially convergent approximation method developed.

In this paper, we establish a sufficient conditions for the nonlocal controllability of mixed VolterraFredholm type fractional semilinear integro-differential inclusions in Banach spaces. The results are obtained by using fractional calculus, operator semigroups and Bohnenblust-Karlin’s fixed point theorem. Finally, an example is given to illustrate the theoretical results.

In this paper, we give some properties of the left and right finite Caputo derivatives. Such derivatives lead to finite Riesz type fractional derivative, which could be considered as the fractional power of the Laplacian operator modelling the dynamics of many anomalous phenomena in super-diffusive processes. Finally, the exact solutions of certain fractional diffusion partial differential equa...

We study the Vladimirov–Taibleson operator, a model example of pseudo-differential operator acting on real- or complex-valued functions defined non-Archimedean local field. prove analogs classical inequalities for fractional Laplacian, counterpart Dirichlet problem including property boundary Hölder regularity solutions.

Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of l...

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...