New results on Caputo fractional-order neutral differential inclusions without compactness

Abstract

This article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations

“…By Lemma 1, we have p(t) ≤ 0 for t ∈ J. Hence, ρ ≡ μ for t ∈ J, and we can conclude ρ ≡ μ ≡ x, in which x is the solution of APBVP (1). e proof of eorem 2 is completed.…”

“…In this section, we apply the quasilinesrization method in order to obtain the result on convergence of the iterative sequences of approximate solutions for APBVP (1).…”

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Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

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