51 citations · 94 across the 10 of their papers we have counts for
10 papers
Asymptotic expansions and approximations for the Caputo derivative
Yuri Dimitrov, Radan Miryanov, Venelin Todorov
In this paper we use the asymptotic expansions of the binomial coefficients and the weights of the L1 approximation to obtain approximations of order and second-order approxi…
Numerical solutions of ordinary fractional differential equations with singularities
Yuri Dimitrov, Ivan Dimov, Venelin Todorov
The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of t…
Approximations for the Caputo Derivative (I)
Yuri Dimitrov
In this paper we construct approximations for the Caputo derivative of order and . The approximations have weights a…
High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation
Yuri M. Dimitrov, Lubin G. Vulkov
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in fin…
Approximations for the Caputo derivative (II)
Yuri Dimitrov, Venelin Todorov, Radan Miryanov
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation…
Higher-Order Numerical Solutions of the Fractional Relaxation-Oscillation Equation using Fractional Integration
Yuri Dimitrov
In the present paper we derive the asymptotic expansion formula for the trapezoidal approximation of the fractional integral. We use the expansion formula to obtain approximations…
Three-Point Compact Approximation for the Caputo Fractional Derivative
Yuri Dimitrov
In this paper we derive the fourth-order asymptotic expansions of the trapezoidal approximation for the fractional integral and the approximation for the Caputo derivative. We…
A New Method for Numerical Solution of the Fractional Relaxation and Subdiffusion Equations Using Fractional Taylor Polynomials
Yuri Dimitrov
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional…
A Second Order Approximation for the Caputo Fractional Derivative
Yuri Dimitrov
When , the approximation for the Caputo derivative where $σ_0^{(α)} = 1, σ_n^{(α)} =…
Numerical Approximations for Fractional Differential Equations
Yuri Dimitrov
The Grünwald and shifted Grünwald formulas for the function are first order approximations for the Caputo fractional derivative of the function with lower limit…