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Many authors have considered and investigated generalized fractional differential operators. The main object of this present paper is to define a new generalized fractional differential operator $mathfrak{T}^{beta,tau,gamma},$ which generalized the Srivastava-Owa operators. Moreover, we investigate of the geometric properties such as univalency, starlikeness, convexity for their normalization. Further, boundedness and compactness in some well known spaces, such as Bloch space for last mention operator also are considered. Our tool is based on the generalized hypergeometric function.
Let $Sinmathcal{M}_d(mathbb{C})^+$ be a positive semidefinite $dtimes d$ complex matrix and let $mathbf a=(a_i)_{iinmathbb{I}_k}in mathbb{R}_{>0}^k$, indexed by $mathbb{I}_k={1,ldots,k}$, be a $k$-tuple of positive numbers. Let $mathbb T_{d}(mathbf a
The aim of this paper is twofold. First, we obtain the explicit exact formal solutions of differential equations of different types in the form with Dyson chronological operator exponents. This allows us to deal directly with the solutions to the equ
Given a sequence of elements $xi={xi_n}_{nin mathbb{N}}$ of a Hilbert space, an operator $T_xi$ is defined as the operator associated to a sesquilinear form determined by $xi$. This operator is in general different to the classical frame operator but
The aim of this paper is to apply generalized operators of fractional integration and differentiation involving Appells function $F_{3}(:)$ due to Marichev-Saigo-Maeda (MSM), to the Jacobi type orthogonal polynomials. The results are expressed in ter
Under a mild Lipschitz condition we prove a theorem on the existence and uniqueness of global solutions to delay fractional differential equations. Then, we establish a result on the exponential boundedness for these solutions.