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In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this
Given a domain $Omega$ in $mathbb{C}^n$ and a collection of test functions $Psi$ on $Omega$, we consider the complex-valued $Psi$-Schur-Agler class associated to the pair $(Omega,,Psi)$. In this article, we characterize interpolating sequences for th
We construct a family $(mathcal{X}_al)_{alle omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $mathcal{X}_al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$.
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution equations of order
In this short note, we first consider some inequalities for comparison of some algebraic properties of two continuous algebra-multiplications on an arbitrary Banach space and then, as an application, we consider some very basic observations on the sp