and Applied Analysis 3 where n α 1, α denotes the integer part of number α, provided that the right side is pointwise defined on 0, ∞ . Definition 2.2 see 20 . The Riemann-Liouville fractional integral of order α > 0 of a function f : 0, ∞ → R is given by I 0 f t 1 Γ α ∫ t 0 t − s α−1f s ds, 2.2 provided that the right side is pointwise defined on 0, ∞ . From the definition of the Riemann-Liouv...

The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

and Dn denotes the derivative operator ∂/∂x1, . . . ,∂xn. The operators in (1.1) provide multidimensional generalizations to the well-known one-dimensional Riemann-Liouville andWeyl fractional integral operators defined in [5] (see also [1]). The paper [7] considers several formulas and interesting properties of (1.1). By invoking the Gauss hypergeometric function 2F1(α,β;γ;x), the following ge...

Fractional derivatives are used to model the transmission of many real world problems like COVID-19. It is always hard find analytical solutions for such models. Thus, approximate interest in interesting applications. Stability theory introduces using some conditions. This article devoted investigation stability nonlinear differential equations with Riemann-Liouville fractional derivative. We e...

Abstract In this paper, we first provide a short summary of the main properties so-called general fractional derivatives with Sonin kernels introduced so far. These are integro-differential operators defined as compositions order derivative and an integral operator convolution type. Depending on succession these operators, Riemann-Liouville Caputo types were studied. The objective paper is cons...

Some power series representations of the modified Bessel functions (McDonald functions Kα) are derived using the little known formalism of fractional derivatives. The resulting summation formulae are believed to be new. 1 Fractional derivatives There are several non-trivial examples in mathematics when some quantity, originally defined as integer, can radically extend its original range and ass...

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...

In the present study, our focus is to obtain different analytical solutions space–time fractional Bogoyavlenskii equation in sense of Jumaries-modified Riemann–Liouville derivative and conformable time–fractional-modified nonlinear Schrödinger that describes fluctuation sea waves propagation water ocean engineering, respectively. The G′G2–expansion method applied investigate dynamics solitons r...

Anomalous dispersion is observed throughout hydrology, yielding a contaminant plume with heavy leading tails. The fractional advection dispersion equation (FADE) captures this behavior by replacing the second-order spatial derivative with a Riemann-Liouville (RL) fractional derivative. The RL fractional derivative is a nonlocal operator and models large jumps of solute particles in heterogeneou...