Open AccessACHIEVING MORE PRECISE BOUNDS BASED ON DOUBLE AND TRIPLE INTEGRAL AS PROPOSED BY GENERALIZED PROPORTIONAL FRACTIONAL OPERATORS IN THE HILFER SENSE
Author(s) -
Maysaa Al-Qurashi,
Saima Rashid,
Yeliz Karaca,
Zakia Hammouch,
Dumitru Băleanu,
YuMing Chu
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x21400272
Subject(s) - mathematics , operator (biology) , differentiable function , fractional calculus , outcome (game theory) , exponential function , kernel (algebra) , function (biology) , type (biology) , calculus (dental) , pure mathematics , mathematical analysis , mathematical economics , ecology , medicine , biochemistry , chemistry , dentistry , repressor , evolutionary biology , biology , transcription factor , gene
A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Čebyšev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Čebyšev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.