scholarly journals A modified Bessel-type integral transform and its compositions with fractional calculus operators on spaces Fp,μ and Fp,μ′

2000 ◽  
Vol 118 (1-2) ◽  
pp. 151-168 ◽  
Author(s):  
H.-J. Glaeske ◽  
Anatoly A. Kilbas ◽  
Megumi Saigo
Keyword(s):  
Fractional Calculus ◽  
Integral Transform ◽  
Type Integral ◽  
Fractional Calculus Operators

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.

On some Hardy-type inequalities for fractional calculus operators

2017 ◽  
Vol 11 (2) ◽  
pp. 438-457 ◽  
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Zivorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

The failure of certain fractional calculus operators in two physical models

2019 ◽  
Vol 22 (2) ◽  
pp. 255-270 ◽  
Author(s):  
Manuel D. Ortigueira ◽  
Valeriy Martynyuk ◽  
Mykola Fedula ◽  
J. Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Human Body ◽  
Real World ◽  
Fractional Derivatives ◽  
Electrical Impedance ◽  
Real Data ◽  
Physical Models ◽  
Data Sets ◽  
Real World Data ◽  
Fractional Calculus Operators

Abstract The ability of the so-called Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) operators to create suitable models for real data is tested with real world data. Two alternative models based on the CF and AB operators are assessed and compared with known models for data sets obtained from electrochemical capacitors and the human body electrical impedance. The results show that the CF and AB descriptions perform poorly when compared with the classical fractional derivatives.

An Application to H2+ of Laplace Type Integral Transform and its Inverse

1985 ◽  
Vol 40 (3) ◽  
pp. 246-250 ◽  
Author(s):  
M. Primorac ◽  
K. Kovačević
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Integral Transform ◽  
Integral Transformation ◽  
Inverse Transform ◽  
Type Integral ◽  
Analytical Formulae ◽  
Molecular Computations ◽  
Laplace Type

Laplace type integral transformation (LIT) has been applied to wavefunctions. The effect of the inverse transform is also discussed. LIT wavefunctions are tested in the calculation of the ground-state energy of H2+, where the untransformed functions were 1s, 12s, 123s and 1234s- STO. The results presented here show that LIT wavefunctions are applicable in molecular computations. The analytical formulae for two-centre one-electron integrals over LIT wavefunctions are derived by use of a Barnett-Coulson-like expansion of rbN (rb + p)-v.

Sign in / Sign up

Export Citation Format

Share Document