Results 221 to 230 of about 290 (254)

OPIAL-TYPE INEQUALITY ABOUT CONFORMABLE FRACTIONAL INTEGRALS AND THE APPLICATION

Fractals, 2021
In this paper, we define partial conformable fractional derivative (PCFD) which is based on the fractional derivative definition proposed by Abdeljawad. At the same time, we present some simple properties about the definition, the properties are useful for us when we carry out further research.
Qi, Yongfang, Li, Guoping, Wang, Xiaoyuan   +2 more
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On Some Special Functions for Conformable Fractional Integrals

2020
In this paper, we introduce the (α,k)-gamma function, (α,k)-beta function, Pochhammer symbol (x)αn,k and Laplace transforms for conformable fractional integrals. We prove several properties generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. The results presented here would provide generalizations of those
SARIKAYA, Mehmet Zeki, AKKURT, Abdullah, BUDAK, Hüseyin, TÜRKAY, Merve Esra, YİLDİRİM, Hüseyin   +4 more
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Conformable fractional integral inequalities of Chebyshev type

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018
The authors derived and proved several new Chebyshev-type inequalities involving new conformable fractional integral operators.
Set, Erhan, Mumcu, İlker, Demirbaş, Sevdenur   +2 more
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Conformable Fractional Approximation by Choquet Integrals

2018
Here we present the conformable fractional quantitative approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study of the conformable fractional rate of the convergence of the well-known Bernstein–Kantorovich–Choquet and Bernstein–Durrweyer–Choquet ...
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New k-Conformable Fractional Integral Inequalities

2020
A new integral identity using the concepts of k-conformable fractional calculus is obtained. Utilizing the preinvexity property of the functions associated upper bounds is also obtained. Some special cases of the obtained results are also discussed.
Muhammad Uzair Awan, Muhammad Aslam Noor, Sadia Talib, Khalida Inayat Noor, Themistocles M. Rassias   +4 more
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Hermite–Hadamard–Fejér inequalities for generalized conformable fractional integrals

Mathematical Methods in the Applied Sciences, 2020
In this paper, we study generalized definitions of left and right conformable fractional derivative and integrals. Some applications of the generalized definition are also given for the nonlinear fractional differential equations. We also establish identities associated with the left‐ and right‐hand side of Hermite–Hadamard–Fejér inequality for ...
Sikander Mehmood, Fiza Zafar, Nusrat Yasmin   +2 more
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CONFORMABLE FRACTIONAL INTEGRALS AND RELATED NEW INTEGRAL INEQUALITIES

2019
In the present note, we have given the definition of conformable fractional integrals and some further properties. In the second part, we have established some Gruss type integral inequalities by using the bounded functions and Lipschitzian mappings via conformable fractional integrals.
Akdemir A.o., Ekinci A., Set E., Akdemir, Ahmet Ocak, Belirlenecek, Akdemir, A.O., Ağrı İbrahim g? University, Faculty of Science and Letters, Department of Mathematics, A?? 04100, Turkey; Ekinci, A., Ağrı İbrahim g? University, Faculty of Science and Letters, Department of Mathematics, A?? 04100, Turkey; Set, E., Ordu University, Faculty of Science and Letters, Department of Mathematics, Ordu, Turkey   +5 more
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REMARKS ON INEQUALITIES WITH PARAMETER BY CONFORMABLE FRACTIONAL INTEGRALS

Fractals
We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established by using the conformable fractional integrals. Namely, we show that our main inequalities reduce to Ostrowski-, Hermite–Hadamard-, Simpson-,
FATIH HEZENCI, MIGUEL VIVAS-CORTEZ, HÜSEYIN BUDAK   +2 more
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INEQUALITIES INVOLVING SPECIAL FUNCTIONS IN CONFORMABLE FRACTIONAL INTEGRALS

In this manuscript, we elucidate essential connections associated with the ( α , k ) − gamma and ( α , k ) − beta functions, initially introduced by Sarikaya et al. in their work as referenced in [14]. Our investigation includes the establishment of numerous conformable fractional integral inequalities, extending those previously ...
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Hermite-Hadamard type inequalities via conformable fractional integrals

2017
New Hermite-Hadamard type inequalities for conformable fractional integrals are derived by using a new identity involving conformable fractional integrals.
Set E., Gözpinar A., Ekinci A., Belirlenecek, Set, E., Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey; Gözpinar, A., Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey; Ekinci, A., Department of Mathematics, Faculty of Science and Letters, Agri Ibrahim Cecen University, Agri, Turkey   +4 more
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