In a rectangular domain, a boundary‐value problem is considered for a mixed equation with
a regularized Caputo‐like counterpart of hyper‐Bessel differential operator and the bi …

Direct and two inverse problems for a Legendre equation involving integral convolution in
time are studied. The inverse problems are ill-posed in the sense of Hadamard. The …

We investigate the initial-boundary value problems for a fourth-order differential equation
within the powerful fractional Dzherbashian-Nersesian operator (FDNO). Boundary …

The paper considers the solvability of some inverse problems for fractional differential
equations with a nonlocal biharmonic operator, which is introduced with the help of …

This paper proposes an approach for the estimation of a time-varying Hurst exponent to
allow accurate identification of multifractional Brownian motion (MFBM). The contribution …

In this paper, we consider a nonlocal boundary-value problem for a mixed-type equation
involving the bi-ordinal Hilfer fractional derivative in a rectangular domain. The main target …

In this paper, we derive a new generalized integral transform on Dzherbashian–Nersesian
fractional operator and give some special cases. We make a generalization of the …

In this paper, in the class of smooth functions, integration and differentiation operators
connected with fractional conformable derivatives are introduced. The mutual reversibility of …

This article primarily aims at introducing a novel operational calculus of Mikusiński's type for
the Dzherbashian‐Nersesian operator. Using this calculus, we are able to derive exact …

A diffusion equation involving integral convolution in time variable with arbitrary kernel and
nonlocal boundary conditions is considered. The existence and uniqueness results for two …