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Start Over Descriptor "fourth-order differential equations" Publication Type Books
2 results on '"fourth-order differential equations"'

1. Nonlinear Differential Equations and Dynamical Systems. Theory and Applications.

Author

Minhós, Feliz Manuel, Fialho, João, and Minhós, Feliz Manuel

Subjects
Mathematics & science, Research & information: general, Caputo operators of different fractional orders, Cauchy problem extremal solutions, Dirac delta function, Laplace transform, Pontryagin extremals, Rosenzweig-MacArthur model, analog of the Saint-Venant principle, basic optimal control problem, boundary value problem, distributed-order fractional calculus, distributional solution, energy estimate, equations of the pseudo-elliptic type of third order, even-order differential equations, existence, fourth-order differential equations, fractional derivatives, hilfer operator, integro-differential equation, inverse problem, mittag-leffler function, mixed type equation, mixed type nonlinear equation, monotone iterative technique, neutral delay, one value solvability, oscillation, power series solution, sign conditions, small parameter, solvability, spectral parameter, spectral parameters, third-order differential equation, threshold harvesting, upper and lower solutions, ψ-Caputo fractional derivative
Abstract

Summary: This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties' oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator-prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

2. Differential Equation Models in Applied Mathematics. Theoretical and Numerical Challenges.

Author

Diele, Fasma and Diele, Fasma

Subjects
Mathematics & science, Research & information: general, Mittag-Leffler function, Sobolev type equation, backward bifurcation, boundary value problems, chemotaxis, dynamical systems, epidemic models, finite difference schemes, food chain, fourth-order differential equations, fractional differential equations, hastings-powell model, high-order equation, hysteresis, indirect methods, inverse problem, linear systems, method of successive approximations, multi-domain network, multi-order systems, n/a, neutral delay, on-off intermittency, optimal control, oscillation, polynomial boundedness of operator pencils, reaction-diffusion models, referral marketing, self-information, stability, stochastic forcing, theoretical ecology, transmission conditions
Abstract

Summary: The present book contains the articles published in the Special Issue "Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges" of the MDPI journal Mathematics. The Special Issue aimed to highlight old and new challenges in the formulation, solution, understanding, and interpretation of models of differential equations (DEs) in different real world applications. The technical topics covered in the seven articles published in this book include: asymptotic properties of high order nonlinear DEs, analysis of backward bifurcation, and stability analysis of fractional-order differential systems. Models oriented to real applications consider the chemotactic between cell species, the mechanism of on-off intermittency in food chain models, and the occurrence of hysteresis in marketing. Numerical aspects deal with the preservation of mass and positivity and the efficient solution of Boundary Value Problems (BVPs) for optimal control problems. I hope that this collection will be useful for those working in the area of modelling real-word applications through differential equations and those who care about an accurate numerical approximation of their solutions. The reading is also addressed to those willing to become familiar with differential equations which, due to their predictive abilities, represent the main mathematical tool for applying scenario analysis to our changing world.

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