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...

The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series

The purpose of this paper is to introduce a modification of q-Dunkl generalization of exponential functions. These types of operators enable better error estimation on the interval [Formula: see text] than the classical ones. We obtain some approximation results via a well-known Korovkin-type theorem and a weighted Korovkin-type theorem. Further, we obtain the rate of convergence of the operato...