We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1 < α ≤ 2. This operator is defined by a combination of the left and right Riemann–Liouville fractional derivatives. We stu...

Using the reviewed Riemann-Liouville fractional derivative we define the bundle αk E = Osc(M) and highlight geometrical structures with a geometrical character. Also, we introduce the fractional osculator Lagrange space of k order and the main structures on it. The results are applied at the k order fractional prolongation of Lagrange, Finsler and Riemann fractional structures. Mathematics Subj...

In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that conditions provided by one-sided Laplace transform not those required for Riemann-Liouville Caputo derivatives. The solved with generality as well applied continuous-time fractional autoregressive-moving average systems.

Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives named after Riemann-Liouville, Caputo Hilfer are shown to be special cases of the earlier one. The expression for Laplace transform constructed. Inverse problems recovering space dependent time source terms a diffusion equation with involution involving considered. results on existence uniquen...

In this article, we investigate partial integrals and derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral derivative order $\gamma = (p, q); p > 0,q 0$, functions are again corresponding to some iterated function system (IFS). Furthermore, discuss transforms

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

The prime aim of the present paper is to continue developing theory tempered fractional integrals and derivatives a function with respect another function. This combines calculus $\Psi$-fractional calculus, both which have found applications in topics including continuous time random walks. After studying basic $\Psi$-tempered operators, we prove mean value theorems Taylor's for Riemann--Liouvi...

While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, situation initial value problems Riemann–Liouville derivatives less understood. In this paper, we propose new type initial, inner, and inner-boundary fractional differential derivatives. The results on existence uniqueness are proved, conditions solvability found. well-posedness of also d...