Browsing by Author "Chu, Yu-Ming"

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Citation - WoS: 17
Citation - Scopus: 19
Achieving More Precise Bounds Based on Double and Triple Integral as Proposed by Generalized Proportional Fractional Operators in the Hilfer Sense
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Al-Qurashi, Maysaa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Cebysev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Cebysev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.
Citation - WoS: 1
Citation - Scopus: 1
A Divided Differences Based Medium To Analyze Smoothness of the Binary Bivariate Refinement Schemes
(Springer, 2021) Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; Hameed, Rabia; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 5
Exact Solutions of the Laplace Fractional Boundary Value Problems Via Natural Decomposition Method
(de Gruyter Poland Sp Z O O, 2020) Khan, Hassan; Chu, Yu-Ming; Shah, Rasool; Baleanu, Dumitru; Arif, Muhammad; Hajira; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs.
Citation - WoS: 27
Citation - Scopus: 29
Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann-Liouville Type
(Hindawi Ltd, 2020) Jarad, Fahd; Chu, Yu-Ming; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we consider the analytic solutions of the uncertain fractional backward difference equations in the sense of Riemann-Liouville fractional operators which are solved by using the Picard successive iteration method. Also, we consider the existence and uniqueness theorem of the solution to an uncertain fractional backward difference equation via the Banach contraction fixed-point theorem under the conditions of Lipschitz constant and linear combination growth. Finally, we point out some examples to confirm the validity of the existence and uniqueness of the solution.
Citation - WoS: 9
Citation - Scopus: 11
Fractional Model of Second Grade Fluid Induced by Generalized Thermal and Molecular Fluxes With Constant Proportional Caputo
(Vinca inst Nuclear Sci, 2021) Ahmad, Mushtaq; Asjad, Muhammad Imran; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.
Citation - WoS: 30
Citation - Scopus: 26
Generalized 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.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 67
Citation - Scopus: 87
Generation of New Fractional Inequalities Via N Polynomials S-Type Convexity With Applications
(Springer, 2020) Iscan, Imdat; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The 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.
Citation - WoS: 86
Citation - Scopus: 107
Inequalities by Means of Generalized Proportional Fractional Integral Operators With Respect To Another Function
(Mdpi, 2019) Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Psi. The authors prove several inequalities for newly defined GPF-integral with respect to another function Psi. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Psi and the proportionality index sigma. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.
Citation - WoS: 1
Citation - Scopus: 1
The Inequalities for the Analysis of a Class of Ternary Refinement Schemes
(Amer inst Mathematical Sciences-aims, 2020) Ejaz, Syeda Tehmina; Baleanu, Dumitru; Chu, Yu-Ming; Mustafa, Ghulam; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The ternary refinement schemes are the generalized version of the binary refinement schemes. This class of the schemes produce the smooth curves with the less number of refinement steps as compared to the binary class of schemes. In this paper, we present the inequalities for the analysis of a class of ternary refinement schemes. There are three simple algebraic expressions in each inequality. Further these algebraic expressions contain only the coefficients used in the refinement rules of the ternary schemes.
Citation - WoS: 12
Citation - Scopus: 12
More New Results on Integral Inequalities for Generalized K-Fractional Conformable Integral Operators
(Amer inst Mathematical Sciences-aims, 2021) Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper aims to investigate the several generalizations by newly proposed generalized K-fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for Cebysev and Polya-Szego type inequalities by generalized K-fractional conformable integral operator. Several special cases are apprehended in the light of generalized fractional conformable integral. This novel strategy captures several existing results in the relative literature. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional integral operator.
New (p, q)-estimates for different types of integral inequalities via (alpha, m)-convex mappings
(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (a alpha, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.p>
New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings
(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (α, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.
Citation - WoS: 7
Citation - Scopus: 7
New (P, Q)-Estimates for Different Types of Integral Inequalities Via (Α, M)-Convex Mappings
(de Gruyter Poland Sp Z O O, 2020) Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Kalsoom, Humaira; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (a alpha, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.
Citation - WoS: 3
Citation - Scopus: 4
A New Approach To Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme
(Hindawi Ltd, 2020) Mustafa, Ghulam; Liaqat, Amina; Baleanu, Dumitru; Khan, Faheem; Al-Qurashi, Maysaa M.; Chu, Yu-Ming; Hameed, Rabia; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up toC3continuity.
A New Approach To Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme (Vol 2020, 6096545, 2020)
(Hindawi Ltd, 2021) Hameed, Rabia; Mustafa, Ghulam; Liaqat, Amina; Baleanu, Dumitru; Khan, Faheem; Al-Qurashi, Maysaa M.; Chu, Yu-Ming; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 49
Citation - Scopus: 64
New Estimates Considering the Generalized Proportional Hadamard Fractional Integral Operators
(Springer, 2020) Rashid, Saima; Jarad, Fahd; Kalsoom, Humaira; Chu, Yu-Ming; Zhou, Shuang-Shuang; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 16
Citation - Scopus: 13
New Estimates of Integral Inequalities Via Generalized Proportional Fractional Integral Operator With Respect To Another Function
(World Scientific Publ Co Pte Ltd, 2020) Hammouch, Zakia; Jarad, Fahd; Chu, Yu-Ming; Rashid, Saima; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, the newly proposed concept of the generalized proportional fractional integral operator with respect to another function phi has been utilized to generate integral inequalities using convex function. This new concept will have the option to reduce self-similitudes in the fractional attractors under investigation. We discuss the implications and other consequences of the integral inequalities concerning the generalized proportional fractional integral operator with respect to another function phi are derived here and these outcomes permit us specifically to generalize some classical inequalities. Certain intriguing subsequent consequences of the fundamental hypotheses are also figured. It is to be supposed that this investigation will provide new directions in the quantum theory of capricious nature.
New Estimates of q1q2 -Ostrowski-Type Inequalities within a Class of n -Polynomial Prevexity of Functions
(2020) Kalsoom, Humaira; Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called n-polynomial preinvex functions. We use the n-polynomial preinvex functions to develop q1q2-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q1q2-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q1q2-analogues of the Ostrowski-type integrals inequalities which are connected with the n-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.
Citation - WoS: 34
Citation - Scopus: 39
New Estimates of Q1q2-Ostrowski Inequalities Within a Class of N-Polynomial Prevexity of Functions
(Hindawi Ltd, 2020) Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-Ming; Kalsoom, Humaira; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is calledn-polynomial preinvex functions. We use then-polynomial preinvex functions to develop q(1)q(2)-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q(1)q(2)-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q(1)q(2)-analogues of the Ostrowski-type integrals inequalities which are connected with then-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.
Citation - WoS: 29
Citation - Scopus: 37
New Generalizations in the Sense of the Weighted Non-Singular Fractional Integral Operator
(World Scientific Publ Co Pte Ltd, 2020) Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose a new fractional operator which is based on the weight function for Atangana{Baleanu (AB)-fractional operators. A motivating characteristic is the generalization of classical variants within the weighted AB-fractional integral. We aim to establish Minkowski and reverse Holder inequalities by employing weighted AB-fractional integral. The consequences demonstrate that the obtained technique is well-organized and appropriate.