scholarly journals ON DISTORTION THEOREMS INVOLVING GENERALIZED FRACTIONAL CALCULUS OPERATORS

1997 ◽  
Vol 27 (3) ◽  
pp. 233-241
Author(s):  
R. K. RAINA ◽  
MAMTA MAMTA EOLIA
Keyword(s):  
Fractional Calculus ◽  
Univalent Functions ◽  
Fractional Integrals ◽  
Generalized Fractional Calculus ◽  
Fractional Calculus Operators ◽  
Distortion Theorems ◽  
Generalized Fractional Calculus Operators ◽  
Analytic And Univalent Functions

This paper gives new classes of distortion inequalities for various sub- classes of analytic and univalent functions. The results presented involve certain generalized fractional integrals of functions belonging to the general classes $J_{\delta}(n)$ and $L_\delta(n)$. Some useful deductions of our main results are also pointed out.

Some generalized fractional calculus operators and their applications in integral equations

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Om Agrawal
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Integral Equations ◽  
Systematic Approach ◽  
Fractional Integrals ◽  
Generalized Fractional Calculus ◽  
Fractional Calculus Operators ◽  
Fractional Integrals And Derivatives ◽  
Generalized Fractional Calculus Operators

AbstractIn this paper, we survey some generalizations of fractional integrals and derivatives and present some of their properties. Using these properties, we show that many integral equations can be solved in a much elegant way. We believe that this will blur the distinction between the integral and differential equations, and provide a systematic approach for the two of these classes.

Application of fractional calculus operators for a new class of univalent functions with negative coefficients defined by Hohlov operator

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Waggas Atshan
Keyword(s):  
Fractional Calculus ◽  
Unit Disc ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
New Class ◽  
Fractional Calculus Operators ◽  
Coefficient Inequalities ◽  
Analytic And Univalent Functions

AbstractIn this paper, we introduce a new class W(a, b, c, γ, β) which consists of analytic and univalent functions with negative coefficients in the unit disc defined by Hohlov operator, we obtain distortion theorem using fractional calculus techniques for this class. Also coefficient inequalities and some results for this class are obtained.

scholarly journals Solvability of some Abel-type integral equations involving the Gauss hypergeometric function as kernels in the spaces of summable functions

2001 ◽  
Vol 43 (2) ◽  
pp. 291-320 ◽  
Author(s):  
R. K. Raina ◽  
H. M. Srivastava ◽  
A. A. Kilbas ◽  
M. Saigo
Keyword(s):  
Fractional Calculus ◽  
Hypergeometric Function ◽  
Integral Equations ◽  
Gauss Hypergeometric Function ◽  
Generalized Fractional Calculus ◽  
Type Integral ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Calculus Operators

AbstractThis paper is devoted to the study of the solvability of certain one-and multidimensional Abel-type integral equations involving the Gauss hypergeometric function as their kernels in the space of summable functions. The multidimensional equations are considered over certain pyramidal domains and the results obtained are used to present the multidimensional pyramidal analogues of generalized fractional calculus operators and their properties.

scholarly journals Certain subclasses of univalent functions and an application of the fractional calculus

2001 ◽  
Vol 32 (2) ◽  
pp. 11-116
Author(s):  
B. A. Uralegaddi ◽  
A. R. Desai
Keyword(s):  
Fractional Calculus ◽  
Univalent Functions ◽  
Special Cases ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

The object of this paper is to obtain some distortion theorems for hte fractional calculus for certain subclasses of analytic and univalent functions. Certain special cases of the results obtained here are also mentioned.

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