Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions by Motlatsi Molati, Chaudry Masood Khalique

“…We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.…”
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A Stability Result for a Swelling Porous System with Nonlinear Boundary Dampings by Adel M. Al-Mahdi, Salim A. Messaoudi, Mohammad M. Al-Gharabli

“…Our result allows a larger class of damping terms, and the usual exponential and polynomial decay estimates are only special cases. …”
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Calculation of bending deflection and stresses of a pipe with flowing fluid in the case of variable ground load by Rimantas Didžgalvis, Antanas Sudintas, Irena Tiknevičienė

“…Using the methods of approximate solutions of differential equations, the analytical pipe bend dynamic expressions were given at the case, when the ground load minimises expo­nentially. Finally, those solutions could be used for the finding more exact normal tensions in the wall of the pipes, when the reological parameters of the ground are determined. …”
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DEVELOPING THE PROGRESSIVE TIME NORMS ON THE OPERATION OF REPAIR MANUFACTURE FOR THE AIRCRAFT ENGINES USING THE EXPERIMENT PLANNING THEORY by A. Tikhonov, A. Komarova

“…Given the example of building the normative dependence as an exponential equation of regression, that allows the influence of both the quantitative and qualitative factors.…”
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Decay Estimates for a Type of Fuzzy Viscoelastic Integro-Differential Model by Fengyun Zhang, Funing Lin, Guangwang Su, Guangming Xue

“…By establishing the estimation of energy function, we derive the stability result of the global solution, and we calculate the estimations of energy attenuation in exponential and polynomial forms, respectively.…”
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C1-Almost Periodic Solutions of BAM Neural Networks with Time-Varying Delays on Time Scales by Yongkun Li, Lili Zhao, Li Yang

“…By employing a fixed point theorem and differential inequality techniques, some sufficient conditions ensuring the existence and global exponential stability of C1-almost periodic solutions for this class of networks with time-varying delays are established. …”
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Analytical Approximant to a Quadratically Damped Duffing Oscillator by Alvaro H. Salas S

“…We give an elementary approximate analytical solution to this oscillator in terms of exponential and trigonometric functions. We compare the analytical approximant with the Runge–Kutta numerical solution. …”
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Antiperiodic Solutions for Quaternion-Valued Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses by Nina Huo, Yongkun Li

“…By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of antiperiodic solutions for QVSICNNs. …”
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Torque Prediction In Deep Hole Drilling: Artificial Neural Networks Versus Nonlinear Regression Model by Ngoc Hung- Chu, Hoai Nam- Nguyen, Van Du- Nguyen, Dang Binh- Nguyen

“…The performance of the ANN model was compared with the exponential model and evaluated by the MAPE index. Results show that the ANN model has better predictive capability, the average MAPE value approximately four times smaller and higher reliability with a standard deviation approximately 3.5 times smaller than the exponential function model. …”
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Minimum Void Ratio Model Established from Tailings and Determination of Optimal Void Ratio by Shibo Li, Hao Liang, Hao Li, Jianquan Ma, Bin Li

“…For tailings, further work is needed to verify if the derived exponential relationship between the optimal void ratio and the equivalent grain size ratio is valid.…”
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Nested Saturation Function Control of a Magnetic Levitation System by Octavio Gutiérrez-Frías, Norma Lozada-Castillo, J. Alejandro Aguirre-Anaya, Diego A. Flores-Hernández

“…The closed-loop error dynamics is proven to be locally exponentially stable. Numerical simulations prove the effectiveness of the proposal.…”
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A Novel Stability Analysis of Uncertain Switched Systems with Time-Varying Delays by Ganji Huang, Shixian Luo, Linna Wei, Wuhua Chen

“…Based on a novel switched time-varying Lyapunov functional method, some new LMI-based sufficient conditions have been obtained to ensure the exponential stability for the uncertain switched delays systems. …”
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The Improved Generalized tanh-coth Method Applied to Sixth-Order Solitary Wave Equation by M. Torvattanabun, J. Simmapim, D. Saennuad, T. Somaumchan

“…The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions, and rational functions solutions. …”
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On Solution of Integrodifferential Equation with Delay Parameter by Sinc Basis Functions by I. Najafi Khalilsaraye, K. Maleknejad

“…So, convergence of this approach is discussed by presenting a theorem which gives exponential type convergence rate and guarantees the accuracy of that. …”
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Investigating the distribution of heat transfer in a thick-walled functionally graded cylindrical shell under heat flux by Buqing Zhang, Zhiqiang Long, Guoqing Liu, Zhengxin Wu, Qiang Yan

“…Abstract The primary aim of this work is to investigate the heat transfer behavior in a thick-walled functionally graded cylindrical shell subjected to internal pressure and thermal gradients, specifically focusing on how different material grading profiles (linear, exponential, and power-law) affect thermal performance. …”
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Potential of CoMn2O4 spinel as soot oxidation catalyst and its kinetics thereof by R. Nithya, Sunaina S. Patil, Hari Prasad Dasari, Harshini Dasari, S. Nethaji

“…This sample demonstrated superior catalytic performance, achieving a T50% of 424 °C, low activation energy (153 kJ/mol) and pre-exponential factor (25 min− 1). Soot TPR analysis highlighted the role of catalyst reducibility, while thermogravimetric analysis revealed that activation energy and pre-exponential factors were influenced by surface composition. …”
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The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the V-Function by S. Chandak, Biniyam Shimelis, Nigussie Abeye, A. Padma

“…In addition, on account of V-function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.…”
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On the Controllability of Conformable Fractional Deterministic Control Systems in Finite Dimensional Spaces by Maher Jneid, Muath Awadalla

“…The present method is based on conformable fractional exponential matrix, Gramian matrix, and the iterative technique. …”
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Lower Confidence Bounds for the Probabilities of Correct Selection by Radhey S. Singh, Narinder Kumar

“…The application of the results to the exponential and normal probability models is discussed. …”
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Stability Conditions of Second Order Integrodifferential Equations with Variable Delay by Dingheng Pi

“…By using the fixed point theory, we obtain conditions which ensure that the zero solution of this equation is stable under an exponentially weighted metric. Then we establish necessary and sufficient conditions ensuring that the zero solution is asymptotically stable. …”
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