scholarly journals m ‐Parameter Mittag–Leffler function, its various properties, and relation with fractional calculus operators

2021 ◽  
Author(s):  
Ritu Agarwal ◽  
Ankita Chandola ◽  
Rupakshi Mishra Pandey ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fractional Calculus ◽  
Fractional Calculus Operators

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.

Extended Mittag-Leffler function and associated fractional calculus operators

2020 ◽  
Vol 27 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Junesang Choi ◽  
Rakesh K. Parmar ◽  
Purnima Chopra
Keyword(s):  
Fractional Calculus ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Fractional Integrals ◽  
Generalized Hypergeometric Function ◽  
Pochhammer Symbol ◽  
Special Cases ◽  
Fractional Calculus Operators ◽  
Fractional Integrals And Derivatives ◽  
Appl Math

AbstractMotivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 2014, 484–491] by means of the generalized Pochhammer symbol, we introduce here a new extension of the generalized Mittag-Leffler function. We then systematically investigate several properties of the extended Mittag-Leffler function including some basic properties, Mellin, Euler-Beta, Laplace and Whittaker transforms. Furthermore, certain properties of the Riemann–Liouville fractional integrals and derivatives associated with the extended Mittag-Leffler function are also investigated. Some interesting special cases of our main results are pointed out.

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