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Integral inequalities involving generalized Erdélyi-Kober fractional integral operators

100%
Baleanu D., Purohit S. D., Prajapati J. C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
89-99
EN
Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.
2
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Results for Mild solution of fractional coupled hybrid boundary value problems

100%
Baleanu D., Jafari H., Khan H., Johnston S. J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.
3
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New properties of conformable derivative

100%
Atangana A., Baleanu D., Alsaedi A.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
Recently, the conformable derivative and its properties have been introduced. In this work we have investigated in more detail some new properties of this derivative and we have proved some useful related theorems. Also, some new definitions have been introduced.
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