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In this paper, a new scheme based on the exponential fitting technique is presented for solving the nonlinear time-fractional Swift-Hohenberg equation, where the first and second-order derivatives are replaced by Caputo fractional derivative. The exponential fitting technique depends on a parameter that led to getting high-order accuracy. The convergence and unconditional stability will be discussed using the Fourier method and the analysis is built on uniform and nonuniform time steps, to solve initial singularity by using the graded meshes. Applicability and theoretical results will be demonstrated and enhanced with numerical examples.

SEIRS epidemic model with Caputo–Fabrizio fractional derivative, a general incidence rate, and the time delay is considered. The main target of this work is to analyze the stability behavior and develop a numerical simulation of the fractional SEIRS model. The reproduction number $${R}_{0}$$ and the order of the fractional derivative $$\beta $$ play an important role in controlling the stability of the equilibrium points of the model, where it was shown that the disease-free equilibrium point $${P}_{0}$$ is asymptotically stable if $${R}_{0}1$$ . The proper choice of the system parameters alongside the order of differentiation guarantee that the epidemic equilibrium point $${P}_{1}$$ is asymptotically stable. The presence of a time delay in treatment and its effect on the stability behavior of the model is considered. Also, bifurcation analysis of the model depending on the time delay, $$ \beta $$ and the treatment rate is discussed. Numerical simulations based on a three-step Adams–Bashforth predictor technique for supporting and validating the theoretical results have been illustrated.

Carbon nano-dots (CDs) are considered nowadays as one of the most interesting fluorescence nanomaterials with various technological applications in almost all aspects of needs e.g., in medicine, biology and engineering. Yet, as reported in many previous works, un-doped CDs suffer from low quantum yield particularly when synthesized at relatively low temperatures. Here, we report on synthesis and characterization of a small size (4.7 nm in diameter) intentionally un-doped CDs with high fluorescence intensity, from Folic Acid as a single precursor, using hydrothermal process at relatively low temperature 200 °C. By attaching organics species of diamine-terminated oligomeric poly-ethylene glycol (PEG) to the surface of the derived CDs, a much stronger photoluminescence from the passivated dots was observed. Namely, we observe a strong enhancement of the CDs quantum yield from 44.4% to 67.5% by varying the PEG concentrations from 0 to 0.2 mM, respectively.

Carbon dots (CDs) have been synthesized hydrothermally from fresh potatoes for the detection of pyridine (PDI) in aqueous solution. The synthesized CDs have been characterized by UV–visible spectrophotometer, FTIR, TEM, and fluorescence measurements. They have a small size of around 11 nm and show a blue emission under UV excitation. The CDs were found to be passivated when mixed with PDI, hence we utilize them as PDI -optical sensor. The detection limit of the of the sensor equals 0.21 µM, which is lower than similar fluorescent sensors in the literature, based on carbon dots synthesized from other sources.

A novel non-local model for studying the performance of solar still system integrated with a photovoltaic panel (PV) using hybrid nanofluid and preheating salty water is presented. The new model is simulated using two different fractional operators: Caputo–Fabrizio and Riemann–Liouville fractional derivatives. The performance of the solar still and photovoltaic panel by using hybrid nanofluid of aluminum oxide and copper oxide (Al2O3/CuO) and using 60%, 50%, and 40% of preheating salty water is also studied. The preheating salty water is implemented as a cooler for the solar cell panel by passing it on the front, back, and both front and back surfaces of the panel before entering the still basin. The obtained results from the two fractional models are compared with the results of a classical model and then compared to data obtained from a real experiment under a meteorological climate condition of Alexandria city, Egypt. The results reveal that the best agreement with the experimental data is obtained based on using Riemann–Liouville fractional derivative with an error of 3.59% unlike the percentage of error which reached 18.9% after using the classical derivative. The findings show that the highest value of the daily still productivity of 6.4099 kg/m2.day is achieved at 60% saline water preheating on the front surface of the PV panel. This value rises to 7.126 kg/m2.day after adding the hybrid nanoparticles (HN) achieving an increase of 10% compared with the system without HN. Moreover, the daily average power of the PV panel reaches 1106.84 W/m2 after using the HN, compared with 988.27 W/m2 without using HN. The maximum average daily energy and exergy efficiencies also occur at 60% of preheating water at the PV front surface with values of 54.61% and 15.3%, respectively, achieving an increase of nearly 10% after using the HN.

Duchenne muscular dystrophy (DMD) is a fatal neuromuscular disorder that occurs due to inactivating mutations in DMD gene, leading to muscular dystrophy. Prediction of pathological complications of DMD and the identification of female carriers are important research points that aim to reduce disease burden. Herein, we describe a case of a late DMD patient and his immediate female family members, who all carry same DMD mutation and exhibited varied degrees of symptoms. In our study, we sequenced the whole miRNome in leukocytes and plasma of the family members and results were validated using real-time PCR. Our results highlighted the role of miR-409-3p, miR-424-5p, miR-144-3p as microRNAs that show correlation with the extent of severity of muscular weakness and can be used for detection of asymptomatic carriers. Cellular and circulating levels of miR-494-3p had shown significant increase in symptomatic carriers, which may indicate significant roles played by this miRNA in the onset of muscular weakness. Interestingly, circulating levels of miR-206 and miR-410-3p were significantly increased only in the severely symptomatic carrier. In conclusion, our study highlighted several miRNA species, which could be used in predicting the onset of muscle and/or neurological complications in DMD carriers.

Duchenne muscular dystrophy (DMD) is one of the fatal X-linked disorders that are characterized by progressive muscle weakness and occur due to mutation in the largest human gene known as the DMD gene which encodes dystrophin protein that is mandatory for keeping the muscles structurally and functionally intact. The disease always affects boys (1 from every ~5000), and in some cases the female carriers are symptomatic. The disease usually leads to impairment in cardiac and pulmonary functions leading to the death of the patients in very young ages. Understanding DMD through precise molecular diagnosis will aid in determining the suitable therapeutic approach for the cases like designing exon-skipping antisense oligonucleotides (AOs) or stem cell-based therapies in conjunction with gene editing techniques (CRISPR/Cas9). Such therapies can correct the genetic defect in the DMD gene and ameliorate the symptoms. In this chapter, we will illustrate the past and current strategies for DMD disease treatment.

In this paper, we consider a cognitive radio networks with secondary users that can choose either to access the idle licensed channel with overlay mode or access the busy licensed channel with semi-passive backscattering mode. A queueing model with heterogeneous service rates is used to derive closed-form expressions for the average number of secondary users in the network and the expected system time for each secondary user. Numerical results are presented to evaluate the system performance improvement due to applying this new setting compared to overlay-only mode and backscattring-only mode. Simulation results are also given to verify the analytical results.

We consider singularly perturbed problems of convection-diffusion-reaction type which involve two small parameters. A new discrete cubic spline method is developed for the solution of this problem on a Shishkin mesh. A convergence analysis is given and the method is shown to be almost second-order uniformly convergent with respect to the perturbation parameters 𝜀d and 𝜀c. Numerical results are presented to validate the theoretical results as well as the robustness of the method.

In this paper, the variable order fractional permanent magnet synchronous motor (VOFPMSM) is investigated.Conditions for existence and uniqueness of the solution of the VOFPMSM are proposed. The stability behavior of the system’sequilibrium points along with the variation of the motor parameters and the order of differentiation is discussed. Sufficient conditionsthat guarantee the asymptotic stability of each of the equilibrium points of the system are established. Also, the required conditions thatgive the effect of Hopf bifurcation of the system are established in terms of the system parameters and the order of differentiation andconsequently the appearance of the chaotic behavior of the VOFPMSM. New numerical techniques based on the modified backwardEuler’s schemes for continuous and discontinuous variable order fractional model are presented. The obtained numerical resultsdemonstrate the merits of the proposed method and the variable order fractional permanent magnet synchronous motor over thefractional permanent magnet synchronous motor.

Carbon quantum dots/polyaniline (CQDs/PANI) nanocomposite was successfully prepared by in-situ polymerization of aniline. CQDs were synthesized hydrothermally from gelatin with a diameter size of 4.2 nm and a 17% quantum yield. FTIR, UV–vis absorption, fluorescence spectrophotometer, XRD, TEM, XPS and lifetime decay were used to characterize the obtained nanocomposite. The formation of PANI revealed a high quenching effect on CQDs where the TEM images showed that the formed CQDs were greatly embedded in PANI matrix. In this study, CQDs/PANI nanocomposite was used for the detection of picric acid (PA) in the range 0.37–1.42 μM with a low detection limit (LOD) of 0.056 μM. The prepared sensor showed good enhancement and sensitivity towards PA in comparison to pristine CQDs and other nanostructured materials. The mechanism of PA detection has been studied where it was observed that PA is electrostatically interacted to the nanocomposite through – OH group of PA and the protonated PANI salt formed in CQDs/PANI nanocomposite by fluorescence resonance energy transfer applications. The proposed CQDs/PANI sensor was then utilized in real water samples and successfully determined the different amounts of PA spiked into tap water.

In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturbation parameter. The proposed method uses interval analysis principle to deal with the uncertain parameter and the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Furthermore, sensitivity analysis has been conducted using different methods to assess how much the solution is sensitive to the changes of the perturbation parameter. Numerical results are provided to show the applicability and efficiency of the proposed method, which is e-uniform convergence of almost second order.

In this article, fractional linear electrical systems are investigated. Analytical solutions of the fractional models are derived using Laplace transform method. Also, numerical simulations using Grunwald–Letnikov definition are proposed. Comparisons between fractional and classical electrical systems are illustrated using Laplace transform and nonstandard finite difference method.

A novel fractional model based on the Riemann Liouville fractional derivative to simulate the thermal performance of conventional solar still and show the effect of using hybrid nanofluid on the desalination system is presented. The results of the fractional model are compared with the results obtained from the classical model, then compared to real experimental data under various climate conditions of Upper Egypt. The theoretical results reveal a perfect agreement between the proposed fractional model and the experimental data of the still with a percentage of error reached 1.486% in summer and 3.243% in winter compared to an error percentage of 24.1% and 20.08%, in case of applying the classical. Moreover, the performance of the modified solar still after adding hybrid nanoparticles is also compared with the conventional solar still. The model is implemented using a hybrid nanofluid of alumina and copper oxide (Al2O3-CuO) with a concentration of 0.025% for each nanoparticle. The results show that using hybrid nanofluid raises the still daily productivity to 5.5239 kg/m2·day in summer and 3.1079 kg/m2·day in winter of an enhancement in the still output yield of 27.2% and 21.7% compared with still without nanoparticles. The average energy efficiency of the still in summer is also increased to 49.54% and 23.212% in summer and winter, respectively, with an augmentation of 12.6% and 11.85% in hot and cold climate conditions, respectively. In addition, the average exergy efficiency is raised by 22.5% in summer and 13.4% in winter by using hybrid nano.

Aniline has been classified as a probable human carcinogen which can cause severe respiratory tract irritation and congestion to humans. Here, we propose using ultra-small (1.8 nm) colloidal nitrogen-doped carbon nano-dots (N-CDs), that is green synthesized at a low temperature of only 100 °C from ultrasonic-processed water-soluble folic acid, as a novel turn-off fluorescent chemo-sensor for ultrasensitive detection of aniline in aqueous medium. It was found that the Stern-Volmer relation describes very well the fluorescence quenching of N-CDs by aniline and confirms a static quenching mechanism between them. Compared to other techniques, our N-CDs based optical detection method, is the simplest and the most ultrasensitive method for aniline liquid detection, reaching an exceptional low detection limit of 3.57 nM (0.332 ppb). The proposed method was successfully applied for determination of aniline in a tap water sample without significant interferences from the matrix.

A modified numerical technique was developed to solve a wide class of variable order fractional optimal control problems in the sense of Riemann Liouville or Caputo derivatives. The modified algorithm is based on the non-standard finite difference method of solving fractional differential equations of variable order. Important property of a reflection operator is used to simplify the variable order right Riemann Liouville or Caputo derivatives to the variable order left Riemann Liouville or Caputo derivatives. Necessary and sufficient conditions that guarantee the existence and the uniqueness of the solution of the resulting systems are given. Illustrative examples are included to demonstrate the validity and the effectiveness of the established approach.

Fluorescent carbon quantum dots (CQDs) have been emerged in countless applications due to their interesting optical, surface properties, and the simplicity of their synthetic routes. On the other hand, pyridine is toxic that could inter into the human living environment causing many health problems, like e.g., asthmatic breathing and laryngitis. Here, water-soluble N-doped CQDs have been synthesized from folic acid and used as chemo-sensor for the determination of pyridine. It was found that pyridine can quench the fluorescence of N-CQDs effectively. The quenching is explained in terms of Stern-Volmer relation and confirmed by fluorescence lifetime measurements to have a dynamic character with a predetermined electron transfer. The detection limit for pyridine was found to be 18 nM. To the best of our knowledge, such a small detection limit is more than three order of magnitude smaller than that obtained so far for pyridine detection using any other facile methods.

Fractional calculus has been increasingly attracting interest in various fields of science and engineering where the problems are governed by differential and integral equations. This shift towards adopting such an approach approves its validity since it has shown that different engineering problems could be better represented by fractional than integer order calculus. Therefore, in this work, fractional calculus is employed in order to simulate a previously addressed problem of metal laser drilling process using meshless local Petrov–Galerkin (MLPG). Both approximations of shifted and weighted shifted Grunwald–Letnikov are used and compared with each other in terms of the expected hole geometry and its closeness to the experimental data. Moreover, the fractional order derivative is considered to be both constant and variable in order to show its impact on the expected outcome of the hole profile. Specifically speaking, for this problem of fixed laser absorptivity, it is shown that the fractional derivative order needs to be variable in order to make the numerical results best match the experimental data in both stages of transient and steady-state.

In this paper, numerical solution of both the combined KdV and modified KdV equation (KdV-MKdV) known as Gardner equation and Harry Dym equation are obtained using quartic B-spline as a space approximation combined with finite difference for time discretization. We also study the stability analysis using Von-Neumann stability analysis showing that the numerical scheme is unconditionally stable. Accuracy of the method is discussed using two test problems. The numerical result shows that the presented method is a successful numerical technique for solving these problems which is showed by presenting the error at different time and space levels.

In this article, a fractional model of HIV/AIDS that includes treatment and a time delay is investigated. The global dynamics of the spread of the disease are discussed using the reproduction number. There is no infected equilibrium if R0 � 1. We also show that the equilibrium point E1 is globally asymptotically stable (the disease disappear) . When R0 > 1, there is a unique infected point E2. We introduce sufficient conditions for the stability of E2. Sufficient conditions are given to guarantee the asymptoti c stability of the equilibria independent of time delay. We present threshold values of the time delay that the treatment will be succeeded if its positive effects appear before this values. A finite difference metho d for a general fractional system is presented and is used in t he numerical simulations of the model.

In this paper, we develop a numerical solution based on nonpolynomial B-spline (trigonometric B-spline) collocation method for solving time-dependent equations involving PHI-Four and Allen–Cahn equations. A three-time-level implicit algorithm has been derived. This algorithm combines the trigonometric B-spline interpolant and the \(\theta \)-weighted scheme for space and time discretization, respectively. Convergence analysis is discussed and the accuracy of the presented method is \(O( {\tau ^{2}+h^{2}} ).\) Applying von Neumann stability analysis, the proposed technique is shown to be unconditionally stable. Three test problems are demonstrated to reveal that our method is reliable, efficient and very encouraging.

The affiliation of the first author W. K. Zahra is Department Engineering Physics and Mathematics, Faculty of Engineering, Tanta University., Tanta, 31521, Egypt.