Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 3Citation - Scopus: 3The Refinement-Schemes Unified Algorithms for Certain Nth Order Linear and Nonlinear Differential Equations With a Set of Constraints(Springer, 2021) Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; Ejaz, Syeda TehminaWe first present a generalized class of binary interpolating refinement schemes and their properties. Then the refinement-schemes-based unified algorithms for the solution of certain nth order linear and nonlinear differential equations with a set of constraints are presented. Moreover, several algorithms based on the refinement schemes for solving differential equations are the special cases of our algorithms.Article Citation - WoS: 70Citation - Scopus: 65On Polya-Szego and Cebysev Type Inequalities Via Generalized K-Fractional Integrals(Springer, 2020) Jarad, Fahd; Kalsom, Humaira; Chu, Yu-Ming; Rashid, Saima; Kalsoom, HumairaIn this paper, we introduce the generalized k-fractional integral in terms of a new parameter k > 0, present some new important inequalities of Polya-Szego and Cebysev types by use of the generalized k-fractional integral. Our consequences with this new integral operator have the abilities to implement the evaluation of many mathematical problems related to real world applications.Article Citation - WoS: 49Citation - Scopus: 64New Estimates Considering the Generalized Proportional Hadamard Fractional Integral Operators(Springer, 2020) Rashid, Saima; Jarad, Fahd; Kalsoom, Humaira; Chu, Yu-Ming; Zhou, Shuang-ShuangIn the article, we describe the Gruss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators.Article Citation - WoS: 31Citation - Scopus: 27Generalized Trapezium-Type Inequalities in the Settings of Fractal Sets for Functions Having Generalized Convexity Property(Springer, 2020) Ashraf, Rehana; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Khan, Zareen A.In the paper, we extend some previous results dealing with the Hermite-Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Holder and power-mean inequalities.As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.Article Citation - WoS: 1Citation - Scopus: 1A Divided Differences Based Medium To Analyze Smoothness of the Binary Bivariate Refinement Schemes(Springer, 2021) Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; Hameed, RabiaIn this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of (m + 1)-point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The C-0, C(1 )and C-2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.Article Citation - WoS: 69Citation - Scopus: 90Generation of New Fractional Inequalities Via N Polynomials S-Type Convexity With Applications(Springer, 2020) Iscan, Imdat; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, SaimaThe celebrated Hermite-Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite-Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing K-fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning.