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Monotonic solutions for quadratic integral equations

Mieczysław Cichoń, Mohamed M.A. Metwali (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

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