Browsing by Author "Baleanu, Dumitru"

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Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(Mdpi, 2017) Acan, Omer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas
In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
Determination of Salicin Content of Some Salix L. Species by Hplc Method
(Chiminform Data S A, 2007) Guvenc, Aysegul; Arihan, Okan; Altun, M. Levent; Dinc, Erdal; Baleanu, Dumitru
In this paper, we find the salicin content of the nine species of Salix L from the province of Ankara, Turkey, namely Salix triandra, S. alba, S. excelsa, S. fragilis, S. babylonica, S. caprea, S. cinerea, S. pseudomedemii and S. amplexicaulis. A simple HPLC method was applied to the determination of Salicin of these nine species in barks and leaves of female and male. Chromatographic separation was carried out by a mobile phase consisting of bidistilled water, tetrahydrofuran and ortho-phosphoric acid (97.7: 1.8: 0.5) (v/v/v). The salicin amount of these samples was analyzed by measuring the peak area at the wavelength, 270 nm. A reversed phase phenyl column (250 x 4.6mm, 5 mu m) was used and flow rate was set to 1 ml/min. in an isocratic elution. The results provided 6 HPLC method was found in agreement with those indicated by European Pharmacopoeia. It was observed that S. babylonica female bark sample possess the highest salicin content (2.675), while S. caprea female bark (0.058) has the lowest salicin content as w/w (%).
Inequalities for N-Class of Functions Using the Saigo Fractional Integral Operator
(Springer-verlag Italia Srl, 2019) Khan, Hasib; Tunc, Cemil; Baleanu, Dumitru; Khan, Aziz; Alkhazzan, Abdulwasea
The role of fractional integral operators can be found as one of the best ways to generalize the classical inequalities. In this paper, we use the Saigo fractional integral operator to produce some inequalities for a class of n-decreasing positive functions. The results are more general than the available classical results in the literature.
On New General Versions of Hermite-Hadamard Type Integral Inequalities Via Fractional Integral Operators With Mittag-Leffler Kernel
(Springer, 2021) Kavurmaci onalan, Havva; Akdemir, Ahmet Ocak; Avci Ardic, Merve; Baleanu, Dumitru
The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite-Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Holder's inequality and Young's inequality, are taken into account in the proof of the findings.
On Solutions of Fractional Riccati Differential Equations
(Springer international Publishing Ag, 2017) Sakar, Mehmet Giyas; Akgul, Ali; Baleanu, Dumitru
We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.