Hyers–Ulam stability for boundary value problem of fractional differential equations with κ-Caputo fractional derivative

The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) via the concept of Caputo fractional derivative with respect to another function with the order $\alpha \in (\mathrm{1,2})$. The existence and uniqueness results of a solution for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide new sufficient conditions to guarantee the Hyers-Ulam stability and the Hyers–Ulam–Rassias stability of BVP-FDEs. Furthermore, some concrete examples to consolidate the obtained results are also considered.     

Reaction of terminal phosphinidene complexes with aldimines: Synthesis of the first 1,2,3-azadiphosphetidine

Transient terminal phosphinidene complexes [RP-M(CO)₅] (M = Mo, W, R = Ph, Me), as generated from the corresponding 7-phosphanorbornadiene complexes, react with N-methyl(benzylidene)amine to afford the diazaphospholane complexes 3,4 (R = Ph) or a mixture of diazaphospholane 9 and 1,2,3-azadiphosphetidine 10 (R = Me), probably by insertion of either one molecule of imine or one molecule of phosphinidene into the weak P N bond of the unstable intermediate azaphosphiridine 11. The new complex 10 has been submitted to an X-ray crystal structure analysis. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9: 597–600, 1998     

Combining phosphinidene units with malonate anion: Synthesis of highly functional phosphine complexes

Malonate anion traps the [RP-W(CO)₅] bridge of 7-phosphanorbornadiene complexes 1–3 to give functional secondary phosphine complexes [RP(H)-CH(CO₂Et)₂]W(CO)₅ ( 7–9 ). Metalation of these complexes by NaH in THF occurs at the malonic CH group, but the alkylation of the resulting carbanions preferentially takes place at phosphorus. When R stands for β-chloroethyl, the corresponding carbanion cyclizes to give the functional phosphirane complex 11 . © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:258–262, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20014     

Improvement in strength of the aluminium/epoxy bonding joint by modification of the interphase

This contribution describes the influence of different surface pre-treatments including self-assembly of phosphoric acid mono alkyl ester as adhesion promoter (AP) for adhesive bonding of aluminium alloy AlMg3. The investigations were performed using a cold hardening two components epoxy-adhesive. The pre-treated surfaces, the interphase structures and the joints were characterized by: SEM/EDX, surface tension, XPS, DMA and the determination of mechanical parameters. The results interestingly show that the test sample with three step pre-treatment (degreasing in acetone, then anodic oxidation in phosphoric acid and adsorption of AP) has the highest adhesive strength and durability.     

Mittag-Leffler stability of random-order fractional nonlinear uncertain dynamic systems with impulsive effects

This paper investigates the Mittag-Leffler stability (MLS) of nonlinear uncertain dynamic systems (NUDSs) with impulsive effects involving the random-order fractional derivative (ROFD) under the fuzzy concept. The major tool used in this paper is Lyapunov’s direct method, which brings high efficiency in surveying the stability theory of dynamic systems. Some algebraic inequalities on the ROFD are established, which is necessary to study the MLS of NUDSs. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.