This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.

This paper presents the Euler–Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the RiemannLiouville fractional derivative.

In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...

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...

and Applied Analysis 3 2. Background Materials and Lemmas For the convenience of the readers, in this section, we provide definitions of RiemannLiouville fractional integral and fractional derivative and some of their basic properties which will be helpful in the forth coming investigations. Definition 2.1 see 2, 5 . For a function φ : a,∞ → R, the Riemann-Liouville fractional integral of order...

One considers a class of fractional random processes defined as non-random dynamics subject to Gaussian white noises in coarse-grained time, according to Maruyama’s notation. After some prerequisites on modified Riemann-Liouville fractional derivative, fractional Taylor’s series and integration with respect to (dx)α , one displays the main results which are as follows: firstly, a general scheme...

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D 0+u(t) + λa(t) f (u(t)) = 0, 0 < t < 1, u(0) = u ′ (0) = u(1) = 0, where 2 < α < 3 is a real number and D 0+ is the standard RiemannLiouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is ...

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order o(ḡ) in the coupling constant ḡ. As a first application, based on the RiemannLiouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non relativistic fractiona...

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...