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.

Among the numerous applications of theory fractional calculus in almost all applied sciences, numerical analysis and various fields physics engineering stand out [...]

The existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators is the topic our paper. researchers used calculus, analysis theory, and Bohnenblust–Karlin’s fixed point theorem for multivalued maps to support their findings. To begin with, we must establish a mild solution. In addition, show principle, an application presented.

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In works, approaches to formulate this are based either on power one Sonin kernel or convolution with kernels integer-order integrals. To apply calculus, it is useful have wider range operators, for example, using Laplace different types kernels. paper, an extended formulation proposed. Ext...

In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.