We study the properties of fractional differentiation with respect to the reflection symmetry in a finite interval. The representation and integration formulae are derived for symmetric and anti-symmetric fractional derivatives, both of the Riemann-Liouville and Caputo type. The action dependent on the left-sided Caputo derivatives of orders in the range (1,2) is considered and we derive the Eu...

This article compares conformable fractional Derivative with Riemann-Liouville and Caputo derivative by comparing solutions to ordinary differential equations involving the three derivatives via numerical simulations of solutions. The result shows that can be used as an alternative for order α 1/2<α<1.

In this paper a new function called as K-function, which is an extension of the generalization of the Mittag-Leffler function[10,11] and its generalized form introduced by Prabhakar[20], is introduced and studied by the author in terms of some special functions and derived the relations that exists between the Kfunction and the operators of Riemann-Liouville fractional integrals and derivatives.

We derive Euler-Lagrange type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order (α, β), α > 0, β > 0, recently introduced by J. Cresson and S. Darses. Some interesting consequences are obtained and discussed. Mathematics Subject Classification 2000: 49K05, 49S05, 70H33, 26A33.

We investigate the profile of the blowing up solutions to the nonlinear nonlocal system (FDS) u′(t) + Dα0+(u − u0)(t) = |v(t)|q, t > 0, v′(t) + Dβ0+(v − v0)(t) = |u(t)|p, t > 0, where u(0) = u0 > 0, v(0) = v0 > 0, p > 1, q > 1 are given constants and Dα0+ and Dβ0+ , 0 < α < 1, 0 < β < 1 stand for the Riemann-Liouville fractional derivatives. Our method of proof relies on comparisons of the solu...

By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.

In this paper, we deal with a coupled system of nonlinear fractional differential equations, which involve the Riemann-Liouville derivatives of different fractional orders. By using the monotone iterative technique combined with the method of upper and lower solutions, we not only obtain the existence of extremal system of solutions, but also establish iterative sequences for approximating the ...

In this paper, a new general identity for differentiable mappings via Riemann-Liouville fractional integrals has been defined. By using of this identity, author has obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolutely value at certain powers are s-convex in the second sense.

In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential Equations into nonlinear ordinary differential Equations. Afterwards, the (Gʹ/G)-expansion method has been implemented, to celeb...

In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard by replacing first- and second-order time derivatives Caputo fractional of corresponding orders, Laplacian operator Sturm–Liouville defined terms right left Riemann–Liouville derivatives. Using method separation variables, derive series representations solut...