Generalized Fractional Calculus Operators and the $$_pR_q(\lambda ,\eta ;z)$$ Function

2020 ◽  
Vol 44 (6) ◽  
pp. 1815-1825
Author(s):  
Ankit Pal ◽  
R. K. Jana ◽  
A. K. Shukla
Keyword(s):  
Fractional Calculus ◽  
Generalized Fractional Calculus ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Calculus Operators

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.

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 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.

scholarly journals Composition Formulas of Bessel-Struve Kernel Function

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Nisar ◽  
S. R. Mondal ◽  
P. Agarwal
Keyword(s):  
Fractional Calculus ◽  
Kernel Function ◽  
Exponential Function ◽  
Integral Representations ◽  
Generalized Fractional Calculus ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Calculus Operators

The object of this paper is to study and develop the generalized fractional calculus operators involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda. Here, we establish the generalized fractional calculus formulas involving Bessel-Struve kernel functionSαλz,  λ,z∈Cto obtain the results in terms of generalized Wright functions. The representations of Bessel-Struve kernel function in terms of exponential function and its relation with Bessel and Struve function are also discussed. The pathway integral representations of Bessel-Struve kernel function are also given in this study.

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