Hausdorff measure of noncompactness of matrix operators on some new difference sequence spaces

Abstract The new sequence spaces X ( r , s , t ; Δ ) $X(r,s,t;\Delta)$ for X ∈ { l ∞ , c , c 0 } $X\in\{l_{\infty}, c, c_{0}\}$ have been defined by using generalized means and difference operator. In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on some new difference sequence spaces X ( r , s , t ; Δ ) $X(r,s,t;\Delta )$ where X ∈ { l ∞ , c , c 0 , l p } $X\in\{l_{\infty}, c, c_{0},l_{p}\}$ ( 1 ≤ p < ∞ $1\leq{p}<\infty$ ), as derived by using generalized means. Further, we find the necessary and sufficient conditions for such operators to be compact by applying the Hausdorff measure of noncompactness. Finally, as applications we characterize some classes of compact operators between these new difference sequence spaces and some other BK-spaces

α-Confluent-hyper-geometric stability of ξ-Hilfer impulsive nonlinear fractional Volterra integro-differential equation

Abstract The purpose of this work is to investigate the necessary conditions for the existence and uniqueness of solutions, and to introduce a new idea of α-confluent-hyper-geometric stability of an impulsive fractional differential equation with ξ-Hilfer fractional derivative. We use the Diaz–Margolis fixed point theorem to achieve this and illustrate the result with an example

Effect of topology on strength and energy absorption of PA12 non-auxetic strut-based lattice structures

With the increasing development of additive manufacturing (AM) technology, lattice structure (LS) emerged and expanded as a subset of cellular materials. LSs' mechanical properties mainly depend on the relative density, the unit cell topology, the manufacturing processes, and the base material. In this research, PA12 lattice structures with non-auxetic strut-based topologies, including BCC, FCC, FCCz, FBCC, FBCCz, FBCCxyz, and OT, were manufactured by selective laser sintering (SLS) and were tested under quasi-static compression. Data from the compression test was analyzed and investigated to achieve mechanical properties such as strength, elastic modulus, and absorbed energy. OT has the highest yield strength (4.07 MPa), ultimate strength (4.53 MPa), specific ultimate strength (10.11 MPa), elastic modulus (0.099 GPa), specific elastic modulus (0.221 GPa), and plateau stress (9.98 MPa) among the investigated sturt-based topologies. BCC has the lowest properties. The absorbed energy (W) for OT and FBCCxyz is higher than in other topologies. FBCCz has the highest volumetric energy absorption (WV) (0.284 MJ/m3) up to the strain of the UTS point, and FCCz has the lowest (0.152 MJ/m3). The finite element method (FEM)-based ABAQUS software was used to simulate the behavior of LSs under compression test. Also, SEM micrographs of struts' fractured surfaces in the CP lattice block were investigated. In most strut-based LSs, the failure mechanism is the layer-by-layer failure of rows. According to finite element modeling results, stress concentration occurred in the nodes and adjacent areas, making cracks, and fractography exhibited ductile fracture in these regions

Existence and Kummer Stability for a System of Nonlinear <i>ϕ</i>-Hilfer Fractional Differential Equations with Application

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems

Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems