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The fractal and fractional calculus have obtained considerable attention in the electrical and electronic engineering since they can model many complex phenomena that the traditional integer-order calculus cannot. The purpose of this paper is to develop a new fractional pulse narrowing nonlinear transmission lines model within the local fractional calculus for the first time and derive a novel method, namely, the direct mapping method, to seek for the nondifferentiable (ND) exact solutions.

By defining some special functions via the Mittag–Leffler function on the Cantor sets, a novel approach, namely, the direct mapping method is derived via constructing a group of the nonlinear local fractional ordinary differential equations. With the aid of the direct mapping method, four groups of the ND exact solutions are obtained in just one step. The dynamic behaviors of the ND exact solutions on the Cantor sets are also described through the 3D graphical illustration.

It is found that the proposed method is simple but effective and can construct four sets of the ND exact solutions in just one step. In addition, one of the ND exact solutions becomes the exact solution of the classic pulse narrowing nonlinear transmission lines model for the special case 9 = 1, which strongly proves the correctness and effectiveness of the method. The ideas in the paper can be used to study the other fractal partial differential equations (PDEs) within the local fractional derivative (LFD) arising in electrical and electronic engineering.

The fractional pulse narrowing nonlinear transmission lines model within the LFD is proposed for the first time in this paper. The proposed method in the work can be used to study the other fractal PDEs arising in electrical and electronic engineering. The findings in this work are expected to shed a light on the study of the fractal PDEs arising in electrical and electronic engineering.

With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).

First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.

The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.

It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.

The fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.

A fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.

The spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.

In the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (S_ff), heat transfer (S_ht) and magnetic field (S_mf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.

It has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Be_ht), fluid friction (Be_ff) and magnetic field (Be_mf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 10² to 10⁴ shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.

Recently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.

The fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

The purpose of this paper is to find a simpler model for the reactance components in the high-frequency range on the premise of ensuring the accuracy.

In this paper, based on the fractional calculus theory and the traditional integer-order model, a reactance model suitable for high frequency is constructed, and the mutation cross differential evolution algorithm is used to identify the parameters in the model.

By comparing the integer-order model, high-frequency fractional-order model and the actual impedance characteristic curve of inductance and capacitance, it is verified that the proposed model can more accurately reflect the high-frequency characteristics of inductance and capacitance. The simulation and experimental results show that the oscillator constructed based on the proposed model can analyze the frequency and output waveform of the oscillator more accurately.

The model proposed in this paper has a simple structure and contains only two parameters to be identified. At the same time, the model has high precision. The fitting errors of impedance curve and phase-frequency characteristic curve are less than 5%. Therefore, the proposed model is helpful to improve the simplicity and accuracy of circuit system analysis and design.

This paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.

Firstly, this paper constructs a new accumulation operation that embodies the new information priority by using a hyperparameter. Then, a new AGSM is constructed by using a new grey action quantity, nonlinear Bernoulli operator, discretization operation, moving average trend elimination method and the proposed new accumulation operation. Subsequently, the marine predators algorithm is used to quickly obtain the hyperparameters used to build the AGSM. Finally, comparative analysis experiments and ablation experiments based on China's quarterly GDP confirm the validity of the proposed model.

AGSM can be degraded to some classical grey prediction models by replacing its own structural parameters. The proposed accumulation operation satisfies the new information priority rule. In the comparative analysis experiments, AGSM shows better prediction performance than other competitive algorithms, and the proposed accumulation operation is also better than the existing accumulation operations. Ablation experiments show that each component in the AGSM is effective in enhancing the predictive performance of the model.

A new AGSM with new information priority accumulation operation is proposed.

Agriculture is the backbone of a country, contributing more than half of the sector of economy throughout the world. The need for precision agriculture is essential in evaluating the conditions of the crops with the aim of determining the proper selection of pesticides. The conventional method of pest detection fails to be stable and provides limited accuracy in the prediction. This paper aims to propose an automatic pest detection module for the accurate detection of pests using the hybrid optimization controlled deep learning model.

The paper proposes an advanced pest detection strategy based on deep learning strategy through wireless sensor network (WSN) in the agricultural fields. Initially, the WSN consisting of number of nodes and a sink are clustered as number of clusters. Each cluster comprises a cluster head (CH) and a number of nodes, where the CH involves in the transfer of data to the sink node of the WSN and the CH is selected using the fractional ant bee colony optimization (FABC) algorithm. The routing process is executed using the protruder optimization algorithm that helps in the transfer of image data to the sink node through the optimal CH. The sink node acts as the data aggregator and the collection of image data thus obtained acts as the input database to be processed to find the type of pest in the agricultural field. The image data is pre-processed to remove the artifacts present in the image and the pre-processed image is then subjected to feature extraction process, through which the significant local directional pattern, local binary pattern, local optimal-oriented pattern (LOOP) and local ternary pattern (LTP) features are extracted. The extracted features are then fed to the deep-convolutional neural network (CNN) in such a way to detect the type of pests in the agricultural field. The weights of the deep-CNN are tuned optimally using the proposed MFGHO optimization algorithm that is developed with the combined characteristics of navigating search agents and the swarming search agents.

The analysis using insect identification from habitus image Database based on the performance metrics, such as accuracy, specificity and sensitivity, reveals the effectiveness of the proposed MFGHO-based deep-CNN in detecting the pests in crops. The analysis proves that the proposed classifier using the FABC+protruder optimization-based data aggregation strategy obtains an accuracy of 94.3482%, sensitivity of 93.3247% and the specificity of 94.5263%, which is high as compared to the existing methods.

The proposed MFGHO optimization-based deep-CNN is used for the detection of pest in the crop fields to ensure the better selection of proper cost-effective pesticides for the crop fields in such a way to increase the production. The proposed MFGHO algorithm is developed with the integrated characteristic features of navigating search agents and the swarming search agents in such a way to facilitate the optimal tuning of the hyperparameters in the deep-CNN classifier for the detection of pests in the crop fields.

Static inverters are very important for the emergency energy distribution system of aircraft and similar machines. At the same time, the electrical energy produced at high frequency for electrical devices is used to reduce the weight of the cables in the aircraft and spacecraft because of the skin effect. In the high-frequency system, a thinner cable cross-section is used, and a great weight reduction occurs in the aircraft. So, fuel economy, less and late wear of the materials (landing gear, etc.) can be obtained with decreasing weight. This paper aims to present the development of a functional multilevel inverter (FMLI) with fractional sinus pulse width modulation (FSPWM) and a reduced number of switches to provide high-frequency and quality electrical energy conversion.

After the production of FSPWM for FMLI with a reduced component, which, to the best of the authors’ knowledge, is presented for the first time in this study, is explained step by step, and eight operating states are given according to different FSPWMs operating the circuit. The designed inverter and modulation technique are compared by testing the conventional modular multilevel inverter on different loads.

According to application results, it is seen that there is a 50% reduction in cross-section from 100 Hz to 400 Hz with the skin effect. At 1000 Hz, there is a 90% cross-section reduction. The decrease can be in cable weights that may occur in aircraft from 10 kg to 100 kg according to different frequencies. It causes less harmonic distortion than conventional converters. This supports the safer operation of the system. Compared to the traditional system, the proposed system provides more amplitude in converting the source to alternating voltage and increases the efficiency.

FSPWM is developed for multilevel inverters with reduced components at the high frequency and cascaded switching studies in the power electronics of aircraft.

Although the proposed system has less current and power loss as mentioned in the previous sections, it contains fewer power elements than conventional inverters that are equivalent for different hardware levels. This not only reduces the cost of the system but also provides ease of maintenance. To reduce the cable load in aircraft and create more efficient working conditions, 400 Hz alternative voltage is used. The proposed system causes less losses and lower harmonic distortions than traditional systems. This will reduce possible malfunctions and contribute to aircraft reliability for passengers and cargo. As technology develops, it is revealed that the proposed inverter system will be more efficient than traditional inverters when devices operating at frequencies higher than 400 Hz are used. With the proposed inverter, safer operation will be ensured, while there will be less energy loss, less fuel consumption and less carbon emissions to the environment.

The proposed inverter structure shows that it can provide energy transmission for electrical devices in space and aircraft by using the skin effect. It also contains less power elements than the traditional inverters, which are equivalent for different levels of hardware.

Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.