Investigation of lump, breather and multi solitonic wave solutions to fractional nonlinear dynamical model with stability analysis by M.A. El-Shorbagy, Sonia Akram, Mati ur Rahman

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On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning by Khalil Ur Rehman, Wasfi Shatanawi, Lok Yian Yian

“…It is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. …”
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On the Weak Characteristic Function Method for a Degenerate Parabolic Equation by Huashui Zhan

“…By this new method, the partial boundary condition matching up with a nonlinear degenerate parabolic equation can be depicted out by an inequality from the diffusion function, the convection function, and the geometry of the boundary ∂Ω itself. …”
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Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation by Shalu Saini, Rajeev Kumar, Kamal Kumar

“…The obtained reduced equation is of fourth order nonlinear ordinary differential equation. …”
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APPROXIMATE SOLUTION FOR BURGER'S-FISHER EQUATION BY VARIATIONAL ITERATION TRANSFORM METHOD by Ali Al-FAYADH

“… Nonlinear partial differential equations represent the most important phenomena occurring in the world and are encountered in various fields of science. …”
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Novel Analytical Methods for and Qualitative Analysis of the Generalized Water Wave Equation by Haitham Qawaqneh, Abdulaziz S. Al Naim, Abdulrahman Alomair

“…Furthermore, the used methods are useful for other nonlinear fractional partial differential equations in different areas of applied science and engineering.…”
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Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 by Hong Li, Hong Yan Xu

“…The purpose of this article is to give the details of finding the transcendental entire solutions with finite order for the systems of nonlinear partial differential-difference equations ∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n1+P1zf2z1+c1,z2+c2m1=Q1z,∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n2+P2zf1z1+c1,z2+c2m2=Q2z, where P1z,P2z,Q1z,andQ2z are polynomials in ℂ2; n1,n2,m1,and m2 are positive integers, and c=c1,c2∈ℂ2. …”
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Adaptive resilient control for a class of nonlinear distributed parameter systems with actuator faults by Hasan Ferdowsi, Jia Cai, Sarangapani Jagannathan

“…This paper presents a new model-based fault resilient control scheme for a class of nonlinear distributed parameter systems (DPS) represented by parabolic partial differential equations (PDE) in the presence of actuator faults. …”
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Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading by Dawei Cheng, Wenke Wang, Xi Chen, Zaiyong Zhang

“…For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. …”
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Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator by Yang Zerong, He Yong

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Impact of the nonlinear thermal radiation on the Arrhenius activation energy of tangent hyperbolic micropolar hybrid nanofluid flow across an extending surface by MD. Shamshuddin, Balasani Srinitha, S.O. Salawu, M. Sunder Ram

“…The energy transmission and fluid flow are mathematically specified using a coupled nonlinear system of PDEs (partial derivative equations). …”
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Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques by Md. Masudar Rahman, S. M. Rayhanul Islam, Ashabul Hoque

“…The study of nonlinear partial differential equations is a crucial area of scientific research to understand fundamental properties and common characteristics of nonlinear phenomena. …”
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Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions by Zakieh Avazzadeh, Mohammad Heydari, Wen Chen, G. B. Loghmani

“…We solve some different type of Urysohn integral equations by using the radial basis functions. …”
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Stagnation-Point Flow toward a Vertical, Nonlinearly Stretching Sheet with Prescribed Surface Heat Flux by Sin Wei Wong, M. A. Omar Awang, Anuar Ishak

“…Both assisting and opposing buoyant flows are considered. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically by finite difference Keller-box method. …”
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Nonlinear Torsional Vibration Analysis of Nanorods in the Presence of Surface Energy Effect: Multi-Mode Galerkin Method by Reza Nazemnezhad, Sahar Farahmandrad

“…For this purpose, Hamilton’s principle is implemented to derive the nonlinear governing equation of motion based on the von-Kármán relations. …”
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Finite Integration Method with Chebyshev Expansion for Shallow Water Equations over Variable Topography by Ampol Duangpan, Ratinan Boonklurb, Lalita Apisornpanich, Phiraphat Sutthimat

“…The method transforms partial differential equations into integral equations, approximates spatial terms via Chebyshev polynomials, and uses forward differences for time discretization. …”
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Abundant closed-form solitary solutions of a nonlinear neurobiological model for analyzing numerous signal transmission behaviors through the neuron using recent scheme by M. Nurul Islam, M. Al-Amin, M. Ali Akbar

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Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method by Mehvish Fazal Ur Rehman, Yongyi Gu, Wenjun Yuan

“…This idea specifies that the extended complex method can acquire exact solutions of several differential equations in engineering. These results reveal that the extended complex method can be directly and easily used to solve further higher-order nonlinear partial differential equations (NLPDEs). …”
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On the “Tantawy Technique” and other methods for analyzing the family of fractional Burgers’ equations: Applications to plasma physics by Aljawhara H Almuqrin, CGL Tiofack, A Mohamadou, Alim Alim, Sherif ME Ismaeel, Weaam Alhejaili, Samir A El-Tantawy

“…We employ these methods to address the complexities associated with fractional partial differential equations (PDEs), specifically using the Caputo operator for fractional derivatives. …”
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Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience by Md. Nur Alam, Md. Azizur Rahman

“…To investigate these soliton solutions, nonlinear fractional differential equations (NLFDEs) are transformed into corresponding partial differential equations (PDEs) using a fractional complex transform (FCT). …”
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