This article studies the existence theory of an innovation type generalized proportional fractional differential equations with assistance technique Kuratowski measure on noncompactness combined fixed-point theorem Mönch. Also, we use Lebesgue’s dominated convergence and Arzelá–Ascoli fixed point uniqueness results. An application is also presented by employing two illustrative iks, which enric...

The present research is concern to the solution of a class mild solutions linked impulsive Hilfer fractional differential equations driven Brownian motion with non-compact semi group in Hilbert spaces. All more obviously Hausdorff measure noncompactness has been utilized get these new results, like manner, arguments were scarred by following tools such as Darbo-Sadovskii fixed point theorem pri...

Abstract. The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of...

Let X be a Banach space, let φ denote the usual Kuratowski measure of noncompactness, and let kX (ε) = sup r (D) where r (D) is the Chebyshev radius of D and the supremum is taken over all closed convex subsets D of X for which diam (D) = 1 and φ (D) ≥ ε. The space X is said to have φ-uniform normal structure if kX (ε) < 1 for each ε ∈ (0, 1) . It is shown that this concept, which lies strictly...

Abstract In this paper, we investigate periodic boundary value problems for Caputo type fractional semilinear nonautonomous differential equations with non-instantaneous impulses. By using semigroup theory combined the measure of noncompactness and some fixed point theorems, existence PC-mild solutions is established. At end, an example presented to illustrate application our main results.

*Correspondence: [email protected] 1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Abstract In this paper, we characterize the matrix classes ( 1, p(F)) (1≤ p <∞), where p(F) is some Fibonacci di...