Global stability for the prion equation with general incidence by Pierre Gabriel

“…We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states.The method is based on the reduction technique introduced in [11].The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.…”
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Integral price formulas for lookback options by Chenglong Xu, Yue Kuen Kwok

“…The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. …”
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A therapy inactivating the tumor angiogenic factors by Cristian Morales-Rodrigo

“…This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. …”
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On Stability of Nonautonomous Perturbed Semilinear Fractional Differential Systems of Order α∈(1,2) by Mohammed M. Matar, Esmail S. Abu Skhail

“…We study the Mittag-Leffler and class-K function stability of fractional differential equations with order α∈(1,2). We also investigate the comparison between two systems with Caputo and Riemann-Liouville derivatives. …”
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C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems by Congcong Shen, Lining Jiang, Zhenhua Ma

“…As an application, we prove the existence and uniqueness of the solution of a type of differential equations.…”
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On a Partial q-Analog of a Singularly Perturbed Problem with Fuchsian and Irregular Time Singularities by Stephane Malek

“…A family of linear singularly perturbed difference differential equations is examined. These equations stand for an analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. …”
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Nonlinear variational evolution inequalities in Hilbert spaces by Jin-Mun Jeong, Doo-Hoan Jeong, Jong-Yeoul Park

“…The regular problem for solutions of the nonlinear functional differential equations with a nonlinear hemicontinuous and coercive operator A and a nonlinear term f(.,.)…”
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Parametrically excited nonlinear systems: a comparison of two methods by A. F. El-Bassiouny

“…Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. …”
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Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems by Chanon Promsakon, Sotiris K. Ntouyas, Jessada Tariboon

“…This paper is concerned with the existence and uniqueness of solutions for a new class of boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented with nonlocal integro-multipoint boundary conditions. …”
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The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes by Yuzhu Xiao, Sufang Tang, Zhongkui Sun

“…Based on the theory of stochastic differential equations, we demonstrate that noise plays a positive role in complete synchronization. …”
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Exact Traveling Wave Solutions to the (2 + 1)-Dimensional Jaulent-Miodek Equation by Yongyi Gu, Bingmao Deng, Jianming Lin

“…It has presented that the applied method is very efficient and is practically well suited for the nonlinear differential equations that arise in mathematical physics.…”
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Thermal effects of ternary Casson nanofluid flow over a stretching sheet: An investigation of Thomson and Troian velocity slip by Musharafa Saleem, A. Al-Zubaidi, Neyara Radwan, S. Saleem, Hind Adawi

“…This leads to a set of partial differential equations (PDEs) based mathematical models transformed into ordinary differential equations (ODEs)-appropriate similarity transformation. …”
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Thermal radiation and thermo-diffusion in Casson-ferrofluid over a magnetized porous surface: RSM analysis by S. Manjunatha, J. Santhosh Kumar, Khalil Ur Rehman, Wasfi Shatanawi, S.V.K. Varma

“…Similarity transformations convert the flow model's governing nonlinear coupled partial differential equations into ordinary coupled differential equations. …”
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RETRACTED: Dynamics of MHD Convection of Walters B Viscoelastic Fluid through an Accelerating Permeable Surface Using the Soret–Dufour Mechanism by P. Anusha, M. Naga Swapna Sri, Vallabhaneni Venkata Venu Madhav, Ch. Sri Chaitanya, V.V. Spandana, Kuldeep K. Saxena, Dalael Saad Abdul-Zahra, Emanoil Linul, Chander Prakash, Dharam Buddhi, Raul Campilho

“…The flow equation constitutes a set of partial differential equations (PDEs) to elucidate the real flow of a non-Newtonian liquid. …”
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RETRACTED ARTICLE: Quadratic multiple regression model and spectral relaxation approach for carreau nanofluid inclined magnetized dipole along stagnation point geometry by Sayed M. El Din, Adil Darvesh, Assad Ayub, Tanveer Sajid, Wasim Jamshed, Mohamed R. Eid, Syed M. Hussain, Manuel Sánchez-Chero, Sheda Méndez Ancca, Johana Milagritos Ramírez Cerna, Carmen Luisa Aquije Dapozzo

“…Physical model generates collection of partial differential equations (PDEs) and these PDEs are moved into ordinary differential equations by a similarity transformations scheme. …”
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Chemical reactions with the Casson nanofluid flow by the bioconvective behavior of microorganisms over a spinning disc by Prabhakar Sagadevan, Umadevi Raju, Meganathan Murugesan, Unai Fernandez-Gamiz, Samad Noeiaghdam

“…Using the right variables to change the nonlinear partial differential equations (PDEs) that govern the problem into a system of ordinary differential equations (ODEs) is a key step toward finding numerical solutions. …”
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Thermodynamics and solar radiative analysis in Jeffery-Hamel flow through non-parallel channel by novel improved residual power series method by Mohamed Bouzidi, Mohsin Ul Haq, Ikram Ullah, Saira Shukat, Hijaz Ahmad, Mohammad Mahtab Alam, Hamid Khan, Marouan Kouki

“…The governing system of partial differential equations can be transformed into ordinary differential equations (ODEs) using suitable transformations. …”
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Mixed convection hybrid nanofluid flow past a non-isothermal cone and wedge with radiation and convective boundary condition: Heat transfer optimization by Rusya Iryanti Yahaya, Norihan Md Arifin, Mohd Shafie Mustafa, Ioan Pop, Fadzilah Md Ali, Siti Suzilliana Putri Mohamed Isa

“…Non-linear ordinary differential equations, derived through similarity transformation of the governing partial differential equations and boundary conditions, are solved numerically using the bvp4c solver. …”
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Impact of nanoparticles shapes and fuzzy volume fraction on Al2O3 – H2O nanofluid flow past an unsteady expandable surface by Adnan Saeed Butt, Naveed Yaqoob, Sameea Akbar, Gul M. Shaikh, Adeeba Farhat, Fouzia Amir, Mohamed R. Ali

“…The goal is to simplify the nonlinear partial differential equations (PDEs) through appropriate transformations, converting them into ordinary differential equations (ODEs). …”
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