A Nonlinear Fractional Problem with Mixed Volterra-Fredholm Integro-Differential Equation: Existence, Uniqueness, H-U-R Stability, and Regularity of Solutions

This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation with a nonlocal initial condition. We propose a fixed-point approach to investigate the existence, uniqueness, and Hyers-Ulam-Rassias stability of solutions. Results of this paper are based on nonstandard assumptions and hypothesis and provide a supplementary result concerning the regularity of solutions. We show and illustrate the wide validity field of our findings by an example of problem with nonlocal neutral pantograph equation, involving functional derivative and ψ -Caputo fractional derivative.

Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls

In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke subdifferential and a fixed point theorem for condensing multivalued maps. Then we present the existence of optimal state-control pairs of the limited Lagrange optimal systems governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. The optimal control results are derived without uniqueness of solutions for the control system.

Approximate Controllability of Semilinear Stochastic Integrodifferential System with Nonlocal Conditions

The objective of this paper is to analyze the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces. The nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskii’s fixed point theorem. At the end, an example is given to show the effectiveness of the result.

Fractional parabolic problems with a nonlocal initial condition

In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problemwhere is a bounded domain, the function a can be a singular potential, g is a suitable function which will be specified later and p, θ Abstract. In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the problem under natural conditions on the data. The question of global existence is also analyzed.