Browsing by Author "Chu, Yu-Ming"

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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
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.
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
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: 38
Citation - Scopus: 30
Prabhakar Fractional Derivative and Its Applications in the Transport Phenomena Containing Nanoparticles
(Vinca inst Nuclear Sci, 2021) Zahid, Muhammad; Chu, Yu-Ming; Baleanu, Dumitru; Asjad, Muhammad Imran
In this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable.
Citation - WoS: 21
Citation - Scopus: 23
Some New Extensions for Fractional Integral Operator Having Exponential in the Kernel and Their Applications in Physical Systems
(de Gruyter Poland Sp Z O O, 2020) Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima
The key purpose of this study is to suggest a new fractional extension of Hermite-Hadamard, Hermite-Hadamard-Fejer and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.
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
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.
NEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACE
(2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (ψ, ?)-convex and approximately ψ-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (ψ, ?)-convex functions such as higher-order strongly (HOS) generalized (ψ, ?)-convex functions and HOS generalized ψ-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (ψ, ?)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized ψ-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields. © 2021 The Author(s).
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
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: 86
Citation - Scopus: 108
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
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: 24
Citation - Scopus: 19
Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function Correlated With Coordinated Generalized Φ-Convex Functions
(Mdpi, 2020) Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Chu, Yu-Ming; Baleanu, Dumitru; Chu, Hong-Hu
In this paper, the newly proposed concept of Raina's function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag-Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q1q2-differentiable function by inserting Raina's functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized phi-convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina's function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.
Citation - WoS: 3
Citation - Scopus: 3
The 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 Tehmina
We 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.
Citation - WoS: 13
Citation - Scopus: 14
New Multi-Functional Approach for Κth-Order Differentiability Governed by Fractional Calculus Via Approximately Generalized (Ψ, (h)over-Bar) Functions in Hilbert Space
(World Scientific Publ Co Pte Ltd, 2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex and approximately psi-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions such as higher-order strongly (HOS) generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions and HOS generalized psi-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized psi-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields.
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
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.
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
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>
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
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
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: 66
Citation - Scopus: 65
A Note on Reverse Minkowski Inequality Via Generalized Proportional Fractional Integral Operator With Respect To Another Function
(Hindawi Ltd, 2020) Jarad, Fahd; Chu, Yu-Ming; Rashid, Saima
This study reveals new fractional behavior of Minkowski inequality and several other related generalizations in the frame of the newly proposed fractional operators. For this, an efficient technique called generalized proportional fractional integral operator with respect to another function phi is introduced. This strategy usually arises as a description of the exponential functions in their kernels in terms of another function phi. The prime purpose of this study is to provide a new fractional technique, which need not use small parameters for finding the approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical results represent that the proposed technique is efficient, reliable, and easy to use for a large variety of physical systems. This study shows that a more general proportional fractional operator is very accurate and effective for analysis of the nonlinear behavior of boundary value problems. This study also states that our findings are more convenient and efficient than other available 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
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.
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
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.
Citation - WoS: 36
Citation - Scopus: 33
Post Quantum Integral Inequalities of Hermite-Hadamard Associated With Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre Mappings
(Mdpi, 2020) Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Akram, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Kalsoom, Humaira
By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard's type inequality and conclude explicit bounds for two new definitions of (p(1)p(2), q(1)q(2))-differentiable function and (p(1)p(2), q(1)q(2))-integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for (p(1)p(2), q(1)q(2))-integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for (p(1)p(2), q(1)q(2))-differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation.
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
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.