A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, the T0periodic PC-mild solution is introduced and suitable Poincaré operator is constructed. Showing the compactness of Poincaré operator and using a new generalized Gronwall inequality with mixed type integral operators ...

The given article describes the implicit fractional dierential equation with anti-periodic boundary conditionsin frame of Caputo-Katugampola derivative. We obtain an analogous integral thegiven problem and prove existence uniqueness results such a using Banach andKrasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, Ulam-Hyersstability are discussed. To show ee...

This paper is devoted to the study of a perturbed differential inclusion governed by nonconvex sweeping process in Hilbert space. The sum an integral forcing term which integrand depends on two time-variables and maximal monotone operator. By using semiregularization method combined with new Pachpatte inequality Gronwall-like we prove solvability initial value problem.

This paper deals with a generalized form of nonlinear retarded Gronwall-Bellman type integral inequality in which the maximum of the unknown function of two variables is involved. This form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. Requiring neither monotonicity nor separability of given functions, we apply a technique of monotonizati...

In the current paper, we consider multi-derivative nonlinear fractional differential equations involving Atangana-Baleanu derivative. We investigate fundamental results about existence, uniqueness, boundedness and dependence of solution on various data. The analysis is based a integral operator due to T. R. Prabhakar generalized Mittag-Leffler function, Krasnoselskii’s fixed point theorem Gronw...

In this paper, we study the existence and uniqueness of mild solutions for nonlinear fractional integro-differential equations (FIDEs) subject to nonlocal integral boundary conditions (nonlocal IBC) in frame a ξ-Hilfer derivative (FDs). Further, discuss different kinds stability Ulam-Hyers (UH) given problem. Using fixed point theorems (FPT's) together with generalized Gronwall inequality desir...

In this paper, a new open-loop PD2D? type fractional order iterative learning control (ILC) is studied for joint space trajectory tracking of linearized uncertain robotic arm. The robust convergent analysis the errors has been done in time domain where it theoretically proven that boundednesses error are guaranteed presence model uncertainty. convergence proposed ILC law mathematically using Gr...