scholarly journals Some general integral inequalities for Lipschitzian functions via conformable fractional integral

2020 ◽  
pp. 952-968
Author(s):  
Sercan TURHAN ◽  
İmdat İŞCAN ◽  
Selim NUMAN
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
General Integral ◽  
Lipschitzian Functions ◽  
Conformable Fractional Integral

scholarly journals The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

2019 ◽  
Vol 52 (1) ◽  
pp. 204-212 ◽  
Author(s):  
Fuat Usta ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Differential Equations ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Inequalities ◽  
Fractional Operator ◽  
Van Der Pol ◽  
Global Existence Of Solutions ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Conformable Fractional Integral

AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

New k-Conformable Fractional Integral Inequalities

2020 ◽  
pp. 35-47
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Sadia Talib ◽  
Khalida Inayat Noor ◽  
Themistocles M. Rassias
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Conformable Fractional Integral

scholarly journals New Modified Conformable Fractional Integral Inequalities of Hermite–Hadamard Type with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Pshtiwan Othman Mohammed ◽  
Artion Kashuri
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Special Means ◽  
Conformable Fractional Integral ◽  
Fractional Parameter

In this study, a few inequalities of Hermite–Hadamard type are constructed via the conformable fractional operators so that the normal version is recovered in its limit for the conformable fractional parameter. Finally, we present some examples to demonstrate the usefulness of conformable fractional inequalities in the context of special means of the positive numbers.

Conformable fractional integral inequalities for some convex functions

2018 ◽  
Vol 27 (2) ◽  
pp. 207-213
Author(s):  
ERHAN SET ◽  
◽  
BARIS CELIK ◽  
ABDURRAHMAN GOZPINAR ◽  
◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral

The main purpose of this paper is to present new Hermite-Hadamard’s type inequalities for functions that belongs to the classes of Q(I), P(I), SX(h, I) and r-convex via conformable fractional integrals . The results presented here would provide extensions of those given in earlier works

scholarly journals New Conformable Fractional Integral Inequalities of Hermite–Hadamard Type for Convex Functions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 263 ◽  
Author(s):  
Pshtiwan Mohammed ◽  
Faraidun Hamasalh
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Conformable Fractional Integral ◽  
New Inequalities

In this work, we established new inequalities of Hermite–Hadamard type for convex functions via conformable fractional integrals. Through the conformable fractional integral inequalities, we found some new inequalities of Hermite–Hadamard type for convex functions in the form of classical integrals.

scholarly journals Some modifications in conformable fractional integral inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Pshtiwan Othman Mohammed ◽  
Miguel Vivas-Cortez ◽  
Yenny Rangel-Oliveros
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Conformable Fractional Integral

scholarly journals Some General Integral Operator Inequalities Associated with φ -Quasiconvex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Young Chel Kwun ◽  
Moquddsa Zahra ◽  
Ghulam Farid ◽  
Praveen Agarwal ◽  
Shin Min Kang
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Quasiconvex Functions ◽  
Operator Inequalities ◽  
Fractional Integral Operators ◽  
General Integral ◽  
General Integral Operator

This paper deals with generalized integral operator inequalities which are established by using φ -quasiconvex functions. Bounds of an integral operator are established which have connections with different kinds of known fractional integral operators. All the results are deducible for quasiconvex functions. Some fractional integral inequalities are deduced.

scholarly journals On generalization conformable fractional integral inequalities

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5519-5526
Author(s):  
Fuat Usta ◽  
Mehmet Sarikaya
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Conformable Fractional Integral ◽  
Conformable Calculus

The main issues addressed in this paper are making generalization of Gronwall, Volterra and Pachpatte type inequalities for conformable differential equations. By using the Katugampola definition for conformable calculus we found some upper and lower bound for integral inequalities. The established results are extensions of some existing Gronwall, Volterra and Pachpatte type inequalities in the previous published studies.

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