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...

At present, fractional differential is the effective mathematical approach which deals with factual problems. This projected technique employs derivatives definitions Riemann-Liouville (R-L), Grunwald-Letnikov (G-L) and caputo for denoising medical image. The presented method based on derivative in turn improves quality of input image processed integer order such as pre-processing operation, co...

We study the existence and uniqueness of solutions for coupled Langevin differential equations fractional order with multipoint boundary conditions involving generalized Liouville–Caputo derivatives. Furthermore, we discuss Ulam–Hyers stability in context problem at hand. The results are shown examples. Results asymmetric when a derivative (ρ) parameter is changed.

We investigate a nonlinear, nonlocal, and fully coupled boundary value problem containing mixed (k,ψ^)-Hilfer fractional derivative (k,ψ^)-Riemann–Liouville integral operators. Existence uniqueness results for the given are proved with aid of standard fixed point theorems. Examples illustrating main presented. The paper concludes some interesting findings.

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

We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and ...

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

Fractional differential equations describe nature adequately because of the symmetry properties that physical and biological processes. In this paper, a new approximation is found for variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on basis, an efficient numerical approach formulated VO time-fractional modified subdiffusion (TFMSDE). Complete theoretical analysis pe...