On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law

The present article deals with a fractional extension of the vibration equation for very large membranes with distinct special cases. The fractional derivative is considered in Atangana-Baleanu sense. A numerical algorithm based on homotopic technique is employed to examine the fractional vibration equation. The stability analysis is conducted for the suggested scheme. The maple software package is utilized for numerical simulation. In order to illustrate the effects of space, time, and order of Atangana-Baleanu derivative on the displacement, the outcomes of this study are demonstrated graphically. The results revel that the Atangana-Baleanu fractional derivative is very efficient in describing vibrations in large membranes.     

Flat sheet direct contact membrane distillation desalination system using temperature-dependent correlations: thermal efficiency via a multi-parameter sensitivity analysis based on Monte Carlo method

Journal of Thermal Analysis and Calorimetry - In this paper, a 1D model of direct contact membrane distillation is presented in which all fluid properties are temperature-dependent. In addition, a...     

Synthesis,characterization of nanosized CoAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and its electrocatalytic activity for enhanced sensing application

Nanosized cobalt aluminate (CoAl₂O₄) was prepared by thermolysis of heteronuclear coordination compound, namely [Al₂Co(C₂O₄)₄(OH₂)₆]. The synthesized precursor was characterized by chemical analysis, vibrational spectra and thermal analysis. The cobalt aluminate obtained after a heating treatment of the precursor at 700 °C was characterized by IR, XRD, TEM coupled with SAED measurements. Two types of carbon-based electrodes, glassy carbon and boron-doped diamond electrodes were decorated with the obtained cobalt aluminate in order to enhance the electroanalytical performance for the tetracycline (TC) detection in the aqueous solutions. Cyclic voltammetry technique was used to determine the effect of the nanosized CoAl₂O₄ on the electrochemical oxidation of TC and as consequence, for TC detection at both carbon-based electrodes. The obtained cobalt aluminate exhibited the electrocatalytic activity toward TC detection in direct relation with the type of the carbon substrate, which allowed enhancing the electroanalytical parameters of TC detection in the aqueous solution.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Reduction in the $$\mathbf {(4+1)}$$(4+1)-dimensional Fokas equation and their solutions

Nonlinear Dynamics - An integrable extension of the Kadomtsev–Petviashvili (KP) and Davey–Stewartson (DS) equations is investigated in this paper. We will refer to this integrable...     

Discrete fractional logistic map and its chaos

A discrete fractional logistic map is proposed in the left Caputo discrete delta’s sense. The new model holds discrete memory. The bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.     

Ternary Copolymerization: Azeotropy and Pseudoazeotropy

An analysis of experimental data for ternary copolymerizations has been performed by an optimizing calculation method, resulting in the estimation of the r _ij copolymerization constants. The azeotrope calculation results have been compared to those based on the r _ij constants found for binary copolymerization. For each set of r _ij constants, the possibility of the ternary azeotropy was studied. The formation of quasihomogeneous ternary copolymers was studied subsequent to the determination of the ternary pseudoazeotropy domains occurring at the intersection of the partial pseudoazeotropy domains.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.