90 research outputs found
Certain subclasses of multivalent functions defined by new multiplier transformations
In the present paper the new multiplier transformations
\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq
0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent
functions is defined. Making use of the operator two new subclasses and \textbf{\ }of multivalent analytic
functions are introduced and investigated in the open unit disk. Some
interesting relations and characteristics such as inclusion relationships,
neighborhoods, partial sums, some applications of fractional calculus and
quasi-convolution properties of functions belonging to each of these subclasses
and
are
investigated. Relevant connections of the definitions and results presented in
this paper with those obtained in several earlier works on the subject are also
pointed out
Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions
In the present investigation, with the help of certain higher- order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the (p, q)-variations is also given in the concluding section
Complex variable approach to analysis of a fractional differential equation in the real line
The first aim of this work is to establish a Peano type existence theorem for
an initial value problem involving complex fractional derivative and the second
is, as a consequence of this theorem, to give a partial answer to the local
existence of the continuous solution for the following problem with
Riemann-Liouville fractional derivative: \begin{equation*} \begin{cases}
&D^{q}u(x) = f\big(x,u(x)\big), \\ &u(0)=b, \ \ \ (b\neq 0). \\ \end{cases}
\end{equation*} Moreover, in the special cases of considered problem, we
investigate some geometric properties of the solutions.Comment: 14 page
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