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1993, Monographs and textbooks in pure and applied mathematics, ISBN 9780824787936, Volume 171., xi, 372
Book
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 06/2017, Volume 29, Issue 2, pp. 615 - 653
In this paper we are concerned with a class of second order abstract neutral functional differential equations with finite delay in a Banach space. We... 
Mild solutions | Second-order abstract Cauchy problems | Cosine functions of operators | Neutral functional differential equations | Classical solutions | EXISTENCE | MATHEMATICS, APPLIED | INTEGRODIFFERENTIAL EQUATIONS | MATHEMATICS | INFINITE DELAY | BANACH-SPACES | SYSTEMS | AUTOMORPHIC SOLUTIONS | Differential equations
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2019, Volume 31, Issue 3, pp. 1247 - 1278
In this paper, we develop the theory of basic reproduction ratios $$\mathcal {R}_0$$ R 0 for abstract functional differential systems in a time-periodic... 
Threshold dynamics | Lyme disease | Mathematics | Periodic solution | 35K57 | 34K20 | 92D30 | Ordinary Differential Equations | Abstract functional differential system | 37B55 | Applications of Mathematics | Partial Differential Equations | Basic reproduction ratio | MATHEMATICS, APPLIED | NUMBERS | PERSISTENCE | STABILITY | MATHEMATICS | SEASONALITY | R-0 | SYSTEMS | EPIDEMIC
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2016, Volume 39, Issue 13, pp. 3897 - 3909
Journal Article
Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 12/2019, Volume 50, Issue 4, pp. 803 - 822
The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the... 
Theoretical, Mathematical and Computational Physics | Uniqueness | Data dependence | Abstract Volterra operator | Mathematics, general | Functional fractional differential equation | Mathematics | Existence | {\varPsi }$$ Ψ -Hilfer fractional derivative
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 216, Issue 1, pp. 61 - 69
We deal in this paper with the mild solution for fractional semilinear differential equations with infinite delay: D α x ( t ) = Ax ( t ) + f ( t , x t , Bx (... 
Mild solution | Infinite delay | Fractional abstract differential equation | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | Mathematical analysis | Differential equations | Images | Uniqueness | Evolution | Mathematical models | Banach space | Delay
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2007, Volume 186, Issue 1, pp. 294 - 301
In this paper, we study the existence of mild solutions for a class of abstract partial neutral functional–differential equations with state-dependent delay. 
Unbounded delay | Neutral equations | Semigroup of linear operators | State-dependent delay | Abstract Cauchy problem | EXISTENCE | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | abstract Cauchy problem | unbounded delay | MODEL | TIME-DELAY | semigroup of linear operators | neutral equations | state-dependent delay | DYNAMICS | STRUCTURED POPULATION-GROWTH | FEEDBACK
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 3/2019, Volume 137, Issue 2, pp. 751 - 812
We describe a new method of constructing transcendental entire functions A such that the differential equation w″ + Aw = 0 has two linearly independent... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | Surgery | Differential equations
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 6/2012, Volume 15, Issue 2, pp. 222 - 231
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 4, pp. 2016 - 2023
We characterize the existence of periodic solutions for a class of abstract retarded functional differential equations with infinite delay. We apply our... 
Abstract functional differential equations | Periodic solutions | UMD spaces | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | PSEUDO | Differential equations | Nonlinear equations | Operators | Images | Nonlinearity | Banach space | Delay
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2014, Volume 2014, Issue 47, pp. 1 - 8
The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence) of the fixed point theory for a functional differential... 
Data dependence | Weakly Picard operators | Functional differential equations | MATHEMATICS | MATHEMATICS, APPLIED | functional differential equations | ABSTRACT VOLTERRA-EQUATIONS | weakly Picard operators | data dependence | weakly picard operators
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 9/2014, Volume 17, Issue 3, pp. 654 - 673
In this paper, we discuss the solutions to nonlocal initial value problems of fractional order functional differential equations in a Banach space. In... 
fractional calculus | functional differential equations | 35A02 | 26A33 | 35A01 | resolvent operator | 34K37 | Mathematics | Integral Transforms, Operational Calculus | 34A08 | 35A09 | Abstract Harmonic Analysis | Functional Analysis | Analysis | 35R11 | EXISTENCE | SPACE | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MILD SOLUTION | DELAY
Journal Article
2004, Lecture notes in mathematics, ISBN 9783540230304, Volume 1855, viii, 472
Book
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 9/2011, Volume 14, Issue 3, pp. 454 - 474
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 6/2014, Volume 17, Issue 2, pp. 348 - 360
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 9/2014, Volume 17, Issue 3, pp. 717 - 744
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 01/2014, Volume 66, Issue 12, pp. 2587 - 2594
In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problems with integral condition for impulsive... 
Abstract spaces | Non-linear fractional differential equations | Existence of solutions | ORDER | MATHEMATICS, APPLIED | FUNCTIONAL-DIFFERENTIAL EQUATIONS | UNIQUENESS | Differential equations
Journal Article
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