Basic results on hybrid differential equations

By Bapurao C. Dhage, V. Lakshmikantham. 2010

223 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/172d72b1bc7f7630ed396cbe20e60a60ffa3a658

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

HYBRID FIXED POINT THEORY IN PARTIALLY ORDERED NORMED LINEAR SPACES AND APPLICATIONS TO FRACTIONAL INTEGRAL EQUATIONS (2013, background): “See Dhage [7], Dhage and Jadhav [9] and the references cited therein.”
Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator (2018, background): “Dhage and Lakshmikantham [15] investigated the EUS to the ordinary hybrid differential equation of first order with perturbation of first type d dt ( u(t) f(t, u(t)) ) = h(t, u(t)), u(t0) = u0 ∈ R, (1.1) where f ∈ C([t0, t0 + a] × R,R − 0), a ∈ R+, [t0, t0 + a] is a bounded interval, f(t, u(t)) is c”
On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations (2020, background): “[2] V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear.”
Basic results in the theory of hybrid differential equations with linear perturbations os second type (2012, background): “[8] B. C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Analysis: Hy- brid Systems, 4 (2010), 414–424.”
On the new fractional hybrid boundary value problems with three-point integral hybrid conditions (2019, background): “First time, in 2010 Dhage and Lakshmikantham introduced hybrid differential equations and proved some basic results on this kind of differential equations [26].”
On Fractional Order Hybrid Differential Equations (2014, background): “D α [ x (t) f (t, x (t)) ] = h (t) , (12) and for the initial condition substitute by t = 0 in (11) we get”
Boundary value problems for hybrid differential equations with fractional order (2015, unknown): “References [1] R. P. Agarwal, V. Lakshmikantham, J. J. Nieto,On the concept of solution for fractional differential equations with uncertainty,Nonlinear Analysis, 72 (2010), 2859-2862.”