Theory of fractional functional differential equations

By V. Lakshmikantham. 2008

554 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6a447e1932ef9f26abffcb2649efca3f9c621157

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Citations in the corpus

SOME EXISTENCE RESULTS FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLINEAR CONDITIONS (2008, background): “In consequence, the subject of fractional differential equations is gaining much importance and attention, see for example [1, 5, 6, 7, 10] and the references therein.”
Dissipativity and Stability Analysis for Fractional Functional Differential Equations (2015, background): “Langlands, Henry, Wearne [19] developed the fractional cable equation models for anomalous electrodiffusion in nerve cells based on many computational and experimental studies and presented the solutions on finite domains.”
Existence of solutions to fractional order ordinary and delay differential equations and applications. (2011, background): “Lakshmikantham and Vatsala in [25, 26] and Lakshmikantham in [27] defined and proved existence of the solution of fractional initial value problems.”
On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations (2020, background): “1 Introduction The classical theory of fractional differential equations (FDEs) relating to inequalities and comparison results has developed by Lakshmikantham et al.[1, 2, 3] and utilized this theory to demonstrate the qualitative and quantitative properties of the solution of various classes of no”
A singular boundary value problem for nonlinear differential equations of fractional order (2009, background): “For only several among numerous advances in the theory and applications of differential equations of fractional order, we refer the reader to [3–7, 11, 15, 16, 20] and the references therein.”
Existence of solutions for fractional differential equations of order q∈(2,3] with anti-periodic boundary conditions (2010, background): “In view of the relations DIx(t) = x(t) and I Ix(t) = I q+px(t) for q,p > 0, x ∈ L(0,1) [9, 13, 16], we obtain x′(t) = ∫ t”
Solving Fractional Delay Differential Equations: A New Approach (2015, background): “Analysis of FDDEs has been carried out [12, 15].”
Stability for Caputo Fractional Differential Systems (2014, background): “[1–5] investigated the basic theory of initial value problems for fractional differential equations involving Riemann-Liouville differential operators of order 0 < q < 1.”