The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation by Hasan Bulut, Haci Mehmet Baskonus, Yusuf Pandir

“…The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. …”
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Implicit numerical technique for solving fractional Navier-Stoks equation with non-singular kernel by L. Azami, A. H. Refahi Sheikhani, H. Saberi Najafi

“…Abstract The nonlinear Burgers equation as a partial differential equation occurs in most physical and mathematical fields such as traffic flow. …”
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Thermal characteristics of hybrid Nanofluid (Cu-Al2O3) flow through Darcy porous medium with chemical effects via numerical successive over relaxation technique by Assmaa Abd-Elmonem, Qammar Rubbab, Hakim AL. Garalleh, Fazeelat Rehman, Muhammad Amjad, Fayza Abdel Aziz ElSeabee, Nesreen Sirelkhtam Elmki Abdalla, Wasim Jamshed, Syed M. Hussain, Hijaz Ahmad

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Generalized J-integral – mathematical foundation by Kohji Ohtsuka

“…Making is done from energy density functions in 2nd-order partial differential equations/systems (PDE/SYS) including nonlinearities and 4th-order PDE using Kirchhoff as an example, where R D ( u ) $R_{D}(u)$ is associated with the Fréchet derivative of an energy functional. …”
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Solitary wave solutions with stability, bifurcation, sensitivity and chaotic analysis of the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation using beta derivative by Saikh Shahjahan Miah, M. Ali Akar, Kamruzzaman Khan

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Exploration of soliton solutions of the nonlinear Kraenkel-Manna-Merle system using innovative methods in ferromagnetic materials by Bahadır Kopçasız, Fatma Nur Kaya Sağlam, Homan Emadifar, Karim K. Ahmed

“…First, a suitable wave transformation is applied to convert the nonlinear partial differential equation (NLPDE) into an ordinary differential equation (ODE). …”
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Case study of radiation absorptive and chemical reactive impacts on unsteady MHD natural convection flowing of Cu-Al2O3/H2O hybridized nanofluid by Rekha Satish, Buchanahalli Thimmaiah Raju, Mummadisetty Umamaheswar, Vijayakumar Varma Sibyala, Charankumar Ganteda, Assmaa Abd-Elmonem, Fayza Abdel Aziz ElSeabee, Neissrien Alhubieshi, Mohamed R. Eid, Wasim Jamshed, Hijaz Ahmad

“…Magnetohydrodynamic hybrid nanofluid (Cu-Al2O3/H2O) flow along an infinitely long plate accelerated exponentially with constant species diffusion, varying heat source and under the chemical reactive, radiation absorptive influences are analysed. Non-dimensional partial differential equation system is derived from the governing nonlinear boundary layer equations. …”
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Formal Diagonalisation of Lax-Darboux Schemes by A. V. Mikhailov

“…We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schro¨dinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral field model as well as with differential-difference integrable systems (including the Toda lattice and differential-difference Heisenberg chain) and integrable partial difference systems. …”
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Additive operator splitting scheme for a general mean curvature flow and application in edges enhancement by Rafaa Chouder, Noureddine Benhamidouche

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Nonlinear Dynamics of Imperfect FGM Conical Panel by Yan Niu, Yuxin Hao, Minghui Yao, Wei Zhang, Shaowu Yang

“…The nonlinear partial differential governing equations are truncated by Galerkin method to obtain the ordinary differential equations along the radial displacement. …”
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Quantum Carleman linearization efficiency in nonlinear fluid dynamics by Javier Gonzalez-Conde, Dylan Lewis, Sachin S. Bharadwaj, Mikel Sanz

“…Here, we try to answer the question of which regimes of nonlinear partial differential equations for fluid dynamics can have an efficient quantum algorithm. …”
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Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams by Yixin Lu, Xiaochao Chen

“…The material properties of beam which vary along both thickness and axial directions follow the power law, and four different distribution patterns are considered. The coupled nonlinear partial differential equations describing the longitudinal-transverse displacements and the shear deformation are derived using Hamilton’s principle based on Timoshenko beam theory. …”
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Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam by W. Gafsi, F. Najar, S. Choura, S. El-Borgi

“…To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. …”
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Nonlinear Vibration Analysis of Damaged Microplate considering Size Effect by Jihai Yuan, Xiangmin Zhang, Changping Chen

“…The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. …”
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Evolution Patterns of Frost-Heaving Pressure with Partial Ponding in Cold Region Tunnels by Xinyu Zheng, Fei Xu, Songtao Shi, Yang Gao, Qi Li

“…The changes in the internal temperature of the surrounding rock and the evolution of the frost-heaving pressure over time under different thicknesses of partial ponding and different levels of surrounding rock were compared. …”
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Nonlinear Torsional Vibration of Size-Dependent Functionally Graded Rods by Reza Nazemnezhad, Ehsan Razavian Shad, Ali-Akbar Jandaghian

“…The von-Kármán type nonlinearity is considered and the governing equation of motion is derived using Hamilton's principle based on the surface elasticity theory. …”
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Data assimilation in 2D hyperbolic/parabolic systems using a stabilized explicit finite difference scheme run backward in time by Alfred S. Carasso

“…An artificial example of a coupled system of three nonlinear partial differential equations generalizing 2D thermoelastic vibrations, is used to demonstrate the effectiveness, as well as the limitations, of a non iterative direct procedure in data assimilation. …”
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Theory of Nonlinear Vibrations for Antisymmetric Cross-Ply Bistable Laminated Shells by B. Y. Zhang, W. Zhang

“…In this paper, on the basis of taking the von Karman nonlinear factors into consideration, the constitutive equation of the antisymmetric cross-ply laminated composite was used to calculate the internal force and internal moment of the bistable structure, and the dynamic equilibrium equation and the compatible equation were constructed, respectively. …”
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Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams by Hu Ding, Li-Qun Chen

“…An integro-partial-differential equation and a partial-differential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. …”
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RESEARCH ON NONLINEAR VIBRATION FOR ELECTRICALLY ACTUATED SINGLE-WALLED CARBON NANOTUBE by YANG ZhiAn, LIU ZhiWei

“…According to the beam theory,the nonlinear dynamic equation of carbon nanotube system is established,it is a nonlinear partial differential equation. …”
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