In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally 1 contracting and TVD. However, the Caputo derivative leads to the modified CFL-type stability condition, ( t) = O( x...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

In this paper the exact and the approximate solutions of fuzzy fractional differential equation, in the sense of Caputo Hukuhara differentiability, with a fuzzy condition are constructed by using the fuzzy Laplace transform. The obtained solutions are expressed in the form of the fuzzy Mittag-Leffler function. The presented procedure is visualized and the graphs of the obtained approximate solu...

The formulations of Riemann-Liouville and Caputo derivatives in the complex plane are presented. Two versions corresponding to the whole or half plane. It is shown that they can be obtained from the Grünwald-Letnikov derivative.

In this paper, we develop a mathematical model with Caputo fractional derivative under fuzzy sense for the prediction of COVID-19. We present numerical results COVID-19 most three infected countries such as USA, India and Italy. Using proposed model, estimate predicting future outbreaks, effectiveness preventive measures potential control strategies infection. provide comparative study Ahmadian...

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

Many dynamic systems can be modeled by fractional differential equations in which some external parameters occur under uncertainty. Although these increase the complexity, they present more acceptable solutions. With aid of Atangana-Baleanu-Caputo (ABC) operator, an advanced numerical-analysis approach is considered and applied this work to deal with different classes fuzzy integrodifferential ...

Fractional control systems with the Caputo derivative are considered. The modified controllability Gramian and the minimum energy optimal control problem are investigated. Construction of minimizing steering controls for the modified energy functional are proposed.

In this article, by using Schaefer fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for a class of impulsive integro-differential equations with nonlocal conditions involving the Caputo fractional derivative.

In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE) of order q ∈ (0,1) under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor’s formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.