In this paper the controllability of a class impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion and Poisson process in separable Hilbert space with infinite delay is studied. The result obtained using analysis fixed-point strategy. Finally, an illustrative example given to demonstrate effectiveness result.

Abstract The Cauchy problem of a time-space fractional partial differential equation which has as particular cases the Klein-Gordon equation, generalized expression heat and two apparently unexplored integro-differential equations in context physics, is proposed solved for delta initial condition. Series H-Fox functions are obtained solution.

Abstract In this paper, we first provide a short summary of the main properties so-called general fractional derivatives with Sonin kernels introduced so far. These are integro-differential operators defined as compositions order derivative and an integral operator convolution type. Depending on succession these operators, Riemann-Liouville Caputo types were studied. The objective paper is cons...

This manuscript focuses on the existence of a mild solution Hilfer fractional neutral integro-differential inclusion with almost sectorial operator. By applying facts related to calculus, semigroup, and Martelli’s fixed point theorem, we prove primary results. In addition, application is provided demonstrate how major results might be applied.

<p style='text-indent:20px;'>We discuss the existence and uniqueness of mild solutions for a class quasi-linear fractional integro-differential equations with impulsive conditions via Hausdorff measures noncompactness fixed point theory in Banach space. Mild solution controllability is discussed two particular cases.</p>

We study the obstacle problem for integro-differential operators of order 2s, with s ∈ (0, 1). Our main result establishes that the free boundary is C and u ∈ C near all regular points. Namely, we prove the following dichotomy at all free boundary points x0 ∈ ∂{u = φ}: (i) either u(x)− φ(x) = c d(x) + o(|x− x0|) for some c > 0, (ii) or u(x)− φ(x) = o(|x− x0|), where d is the distance to the con...

Reaction-diffusion equations are commonly used to model the growth and spreading of biological species. The classical diffusion term implies a Gaussian dispersal kernel in the corresponding integro-difference equation, which is often unrealistic in practice. In this paper, we propose a fractional reaction-diffusion equation where the classical second derivative diffusion term is replaced by a f...

This work presents a projection method based on Vieta–Lucas polynomials and an effective approach to solve Cauchy-type fractional integro-differential equation system. The suggested established model overcomes two linear systems. We prove the existence of problem’s approximate solution conduct error analysis in weighted space. theoretical results are numerically supported.

In this paper, we study a new approach of investigation existence, uniqueness and stability the periodic solution nonlinear fractional integro-differential equation type Caputo-Fabrizio derivative with initial condition, boundary conditions, integral conditions by using successive approximations method Banach fixed point theorem. Finally, some examples are present to illustrate theorems.