An abstract causal operator equation y = Ay defined on a space of the form L1([0, τ ], X), with X a Banach space, is regularized by the fractional differential equation ε(D 0 yε)(t) = −yε(t) + (Ayε)(t), t ∈ [0, τ ], where Dα 0 denotes the (left) Riemann-Liouville derivative of order α ∈ (0, 1). The main procedure lies on properties of the Mittag-Leffler function combined with some facts from co...

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called Mittag-Leffler–Galerkin method—comprises finite Mittag-Leffler function and Galerkin method. error analysis of method was studied. As result, we two theorems by which can be bounded. In addition analysis, residual correction method, allows us estimate obtain approximate ...

This paper deals with the study of linear systems of fractional differential equations such as the following system: 0096-3 doi:10 * Co E-m Y ða 1⁄4 AðxÞY þ BðxÞ; ð1Þ where Y ða is the Riemann–Liouville or the Caputo fractional derivative of order a (0 < a 5 1), and AðxÞ 1⁄4 a11ðxÞ a1nðxÞ . . . . . . . . . an1ðxÞ annðxÞ 0BBBBBB@ 1CCCCCCA; BðxÞ 1⁄4 b1ðxÞ . . . . . . . . . bnðxÞ 0BBBBBB@ 1CCCCCCA...

*Correspondence: [email protected] 3Department of Mathematical Sciences, UAE University, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involvin...