In this paper, we study linear fractional fuzzy differential equations involving the Caputo generalized Hukuhara derivative. Using the fuzzy Laplace transform, we present the general form of solutions in terms of Mittag-Leffler functions. Finally, some examples are provided to illustrate our results.

In this paper, several integral inequalities for the functions whose derivatives are s-convex functions in the fourth sense are obtained by means of Caputo fractional derivative and Caputo-Fabrizio integral operator. Also the Hermite-Hadamard type inequalities for s-convex functions and their products are stated via Caputo-Fabrizio integral operator.

‎This paper presents the visualization process of finding the roots of a complex polynomial‎ - ‎which is called polynomiography‎ - ‎by the Caputo fractional derivative‎. ‎In this work‎, ‎we substitute the variable-order Caputo fractional derivative for classic derivative in Newton's iterative method‎. ‎To investigate the proposed root-finding method‎, ‎we apply it for two polynomials $p(z)=z^5-1$ and $ p(z)=-2z^4+z^3+z^2-2z-1 $ on the complex plane and compute the MNI and CAI parameters‎.‎Presented examples show that through the expressed process‎, ‎we can obtain very interesting fractal patterns‎. ‎The obtained patterns show that the proposed method has potential artistic application‎.

The aim of this study is to establish some new Caputo frac-tional integral inequalities. By applying de, nition of (h􀀀, m)-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Fur-thermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from (h 􀀀,m)-convexity, see Remark 1. 3.

In the paper, we consider a type of Cattaneo equation with time fractional derivative without singular kernel based on fourth-order compact finite difference (CFD) in the space directions. In case of two dimensional, two alternating direction implicit (ADI) methods are proposed to split the equation into two separate one dimensional equations. The time fractional derivation is described in the Caputo-Fabrizio’s sense with scheme of order O(τ2). The solvability, unconditional stability and H1 norm convergence of the scheme are proved. Numerical results confirm the theoretical results and the effectiveness of the proposed scheme.

This article deals with the existence, uniqueness and Ulam type stability results for a class of boundary value problems for fractional differential equations with Riesz-Caputo fractional derivative. The results are based on Banach contraction principle and Krasnoselskii's fixed point theorem. An illustrative example is given to validate our main results.

The present article introduces an operational approach based on modified hat functions to solve the space-time-fractional differential equations in the Caputo sense. In this method, the derivative of the unknown function is considered as a linear combination of modified hat functions. We use the operational matrix of the Riemann–Liouville fractional integral of modified hat functions to approximate the Caputo fractional derivative in order to reduce the problem to a system of Sylvester equations. The error of the mentioned method is of the order O(h3). In addition, we examine several  numerical examples to confirm the ability of the proposed approach.