Browsing by Author "Agarwal, Praveen"

Now showing 1 - 9 of 9

Citation - WoS: 58
Citation - Scopus: 58
Certain Hermite-Hadamard Inequalities for Logarithmically Convex Functions With Applications
(Mdpi, 2019) Mehrez, Khaled; Baleanu, Dumitru; Agarwal, Praveen; Jain, Shilpi; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite-Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.
Citation - WoS: 18
Citation - Scopus: 28
Certain Inequalities Involving the Fractional Q-Integral Operators
(Hindawi Ltd, 2014) Agarwal, Praveen; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We establish some inequalities involving Saigo fractional q-integral operator in the theory of quantum calculus by using the two parameters of deformation, q(1) and q(2), whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville and Kober fractional q-integral operators, respectively. Furthermore, we also consider their relevance with other related known results.
Citation - WoS: 3
Citation - Scopus: 3
Certain New Gruss Type Inequalities Involving Saigo Fractional Q-Integral Operator
(Eudoxus Press, Llc, 2015) Wang, Guotao; Baleanu, Dumitru; Agarwal, Praveen; Baleanu, Dumitru; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the present paper, we aim to investigate a new q-integral inequality of Gruss type for the Saigo fractional q-integral operator. Some special cases of our main results are also provided. The results presented in this paper improve and extend some recent results.
Citation - WoS: 11
Citation - Scopus: 13
A Composition Formula of the Pathway Integral Transform Operator
(Aracne Editrice, 2014) Agarwal, Praveen; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the present paper, we aim at presenting composition formula of integral transform operator due to Nair, which is expressed in terms of the generalized Wright hypergeometric function, by inserting the generalized Bessel function of the first kind w(v) z). Furthermore the special cases for the product of trigonometric functions are also consider.
Citation - WoS: 26
Extension of the Fractional Derivative Operator of the Riemann-Liouville
(int Scientific Research Publications, 2017) Agarwal, Praveen; Parmar, Rakesh K.; Alqurashi, Maysaa M.; Salahshour, Soheil; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions. (C) 2017 All rights reserved.
Citation - WoS: 21
Citation - Scopus: 31
New Fractional Inequalities of Hermite-Hadamard Type Involving the Incomplete Gamma Functions
(Springer, 2020) Baleanu, Dumitru; Kashuri, Artion; Hamasalh, Faraidun; Agarwal, Praveen; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A specific type of convex functions is discussed. By examining this, we investigate new Hermite-Hadamard type integral inequalities for the Riemann-Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.
Citation - WoS: 2
Non-Conformable Integral Inequalities of Chebyshev-Polya Type
(Element, 2021) Akdemir, Ahmet Ocak; Agarwal, Praveen; Baleanu, Dumitru; Butt, Saad Ihsan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Inequality studies involving new integrals and derivatives have been carried out recently. This article designed as follows, the results were obtained by using the non-conformable fractional integral operators to provide new inequalities of Polya-Szego and Chebyshev type. Some special cases have been considered for our main findings.
Citation - WoS: 137
Citation - Scopus: 154
On Analytical Solutions of the Fractional Differential Equation With Uncertainty: Application To the Basset Problem
(Mdpi, 2015) Ahmadian, Ali; Senu, Norazak; Baleanu, Dumitru; Agarwal, Praveen; Salahshour, Soheil; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we apply the concept of Caputo's H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann-Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
Citation - WoS: 12
Citation - Scopus: 24
On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions
(Hindawi Ltd, 2014) Agarwal, Praveen; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A remarkably large number of fractional integral formulas involving the number of special functions, have been investigated by many authors. Very recently, Agarwal (National Academy Science Letters) gave some integral transform and fractional integral formulas involving the F-P((alpha,beta)) (.), In this sequel, here, we aim to establish some image formulas by applying generalized operators of the fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda. Some interesting special cases of our main results are also considered.