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- Univalent Functions and Teichmuller Spaces.
- Graduate Texts in Mathematics
- Springer Graduate Texts in Mathematics (GTM)
- yfonyhmagso.tkonal analysis - Topological vector space textbook with enough applications - MathOverflow

In this paper, we consider various classes of degenerate k-regularized C 1 , C 2 -existence and uniqueness families. The main purpose of the paper is to report how the techniques established in a joint paper of C. Li, M. Li and the author [32] can be successfully applied in the analysis of a wide class of abstract degenerate multi-term fractional differential equations with Caputo derivatives. Keywords and Phrases: Abstract multi-term fractional differential equations, degenerate differential equations, fractional calculus, Mittag-Leffler functions, Caputo time-fractional derivatives.

Abdelaziz and F.

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Agarwal, B. Cuevas, Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Anal.

Aliev and B. Lichaei, Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations, Nonlinear Anal. Arendt, C. Batty, M. Hieber and F.

## Univalent Functions and Teichmuller Spaces.

Balaev, Higher order parabolic type evolution equations, Dokl. Azerbaidjan 41 , Russian. Bazhlekova, Fractional evolution equations in Banach spaces, Ph. Carroll and R. Cuevas and C. Lizama, Almost automorphic solutions to a class of semilinear fractional differential equations, Appl. Cuevas, M.

## Graduate Texts in Mathematics

Pierri and A. London Math. Demidenko and S. Diagana and G. Falaleev and S. Favini and A.

Fedorov and A. Debbouche, A class of degenerate fractional evolution systems in Banach spaces, Differential Equations 49 , Fedorov and D. Gordievskikh, Resolving operators of degenerate evolution equations with fractional derivative with respect to time, Izv. Fedorov, On solvability of perturbed Sobolev type equations, St. Petersburg Math.

Fedorov, M. Kilbas, H. Key topics covered include point set topology, topological vector spaces, the Hahn? Banach theorem, seminorms and Frechet spaces, uniform boundedness, and dual spaces.

### Springer Graduate Texts in Mathematics (GTM)

The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course. Smulian Theorem. Develops of a new interval theory Presents several sample applications Includes many examples to illustrate the main results This book presents an innovative new approach to interval analysis. Modal Interval Analysis MIA is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features.

The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals through the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions.

Applications of these equivalences in different areas illustrate the obtained results.

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The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computations. Develops a class of spatial models of a population undergoing mutation, selection and migration Develops new duality methods for multitype population models Develops the McKean-Vlasov limit of exchangeable population models and their entrance laws Identifies mutation-selection equilibria Offers valuable insights into the role of migration in the emergence of rare mutants in spatial Fleming-Viot models Sheds new light on the role of migration in sustaining biodiversity in evolution This book constructs a rigorous framework for analysing selected phenomena in evolutionary theory of populations arising due to the combined effects of migration, selection and mutation in a spatial stochastic population model, namely the evolution towards fitter and fitter types through punctuated equilibria.

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## yfonyhmagso.tkonal analysis - Topological vector space textbook with enough applications - MathOverflow

The discussion is based on a number of new methods, in particular multiple scale analysis, nonlinear Markov processes and their entrance laws, atomic measure-valued evolutions and new forms of duality for state-dependent mutation and multitype selection which are used to prove ergodic theorems in this context and are applicable for many other questions and renormalization analysis for a variety of phenomena stasis, punctuated equilibrium, failure of naive branching approximations, biodiversity which occur due to the combination of rare mutation, mutation, resampling, migration and selection and make it necessary to mathematically bridge the gap in the limit between time and space scales.

Nonlinear semigroup perturbations.

The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book.

The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.