Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order by Ming Li, Wei Zhao

“…This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. …”
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The Asymptotic Behaviours of a Class of Neutral Delay Fractional-Order Pantograph Differential Equations by Baojun Miao, Xuechen Li

“…By using fractional calculus and the summation by parts formula in this paper, the asymptotic behaviours of solutions of nonlinear neutral fractional delay pantograph equations with continuous arguments are investigated. …”
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The Use of Spreadsheets for Pharmacokinetic Simulations by Joseph Chamberlain

“…The basics of spreadsheets are first described and are developed to demonstrate classical pharmacokinetics without the use of differential or integral calculus. Using standard spreadsheet commands, the technique is shown to be applicable to the full range of advanced pharmacokinetic simulations. …”
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On the Total Electronic Density of States of Disordered Solids by M. A. Grado-Caffaro, M. Grado-Caffaro

“…The concept of total electronic density of states calculated for small clusters in amorphous solids is presented in a new way by using a mathematical formulation based upon matrix calculus. Furthermore, the associated Green's function is discussed in a special form. …”
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New classification of analytic functions with negative coefficients by Shigeyoshi Owa, Milutin Obradovic

“…The object of the present paper is to prove various distortion theorems for functions in A(p,n,Bk), and for fractional calculus of functions belonging to A(p,n,Bk). Further, some properties of the class A(p,n,Bk) are shown.…”
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Time Scale Inequalities of the Ostrowski Type for Functions Differentiable on the Coordinates by Eze R. Nwaeze, Seth Kermausuor, Ana M. Tameru

“…Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction.…”
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Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives by Ali El Mfadel, Said Melliani, M’hamed Elomari

“…In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.…”
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Integration by Parts and Martingale Representation for a Markov Chain by Tak Kuen Siu

“…Integration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integration-by-parts formulas. …”
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Promoting Healthy Relationship Development in Teens, Part I: How Dating Smart in Youth Can Foster Better Relationships in Adulthood by Victor William Harris, Gilon Marts, Martie Gillen

“…Cultivating healthy dating relationships that can lead to healthy adult romantic and marriage relationships is a science that reflects a complicated calculus of the premarital influences that may shape future relationship stability, quality, and satisfaction. …”
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A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation by Li Yao, Yun-Jie Yang, Xing-Wei Zhou

“…Ji-Huan He systematically studied the inverse problem of calculus of variations. This note reveals that the semi-inverse method also works for a generalized KdV-mKdV equation with nonlinear terms of any orders.…”
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Promoting Healthy Relationship Development in Teens, Part I: How Dating Smart in Youth Can Foster Better Relationships in Adulthood by Victor William Harris, Gilon Marts, Martie Gillen

“…Cultivating healthy dating relationships that can lead to healthy adult romantic and marriage relationships is a science that reflects a complicated calculus of the premarital influences that may shape future relationship stability, quality, and satisfaction. …”
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The Solvability and Optimal Controls for Some Fractional Impulsive Equation by Xianghu Liu, Zhenhai Liu, Jiangfeng Han

“…Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. …”
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Generalized classes of starlike and convex functions of order α by Shigeyoshi Owa, C. Y. Shen

“…We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. …”
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Zacharij Niemcevski – professor of higher mathematics at the Vilnius university (1797–1820) by Evaldas Gečiauskas

“…Niemcevski tought differential and integral calculus by the tracktate of S.F. Lacroix, analytic geomety – by J.B. …”
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Clostridium tetani bacteraemia in the plague area in France: Two cases by M.A. Boualam, A. Bouri, M. Signoli, M. Drancourt, A. Caputo, E. Terrer, G. Aboudharam

“…In the remaining twelve individuals, no such C. tetani was recovered and further detection by PCR and palaeoculturomics of dental calculus and sediments surrounding the teeth in these two individuals remained negative. …”
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Candida albicans Fungaemia following Traumatic Urethral Catheterisation in a Paraplegic Patient with Diabetes Mellitus and Candiduria Treated by Caspofungin by Subramanian Vaidyanathan, Bakul Soni, Peter Hughes, Gordon Ramage, Leighann Sherry, Gurpreet Singh, Paul Mansour

“…Computed tomography of abdomen revealed inflamed uroepithelium of right renal pelvis and ureter, 4 mm lower ureteric calculus with gas in right ureter proximally, and vesical calculus containing gas in its matrix. …”
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-Dimensional Fractional Lagrange's Inversion Theorem by F. A. Abd El-Salam

“…The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. …”
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Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space by Mabrouk Bragdi, Amar Debbouche, Dumitru Baleanu

“…In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.…”
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Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications by Soo Hwan Kim

“…We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. …”
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Adaptation of Differential Transform Method for the Numeric-Analytic Solution of Fractional-Order Rössler Chaotic and Hyperchaotic Systems by Asad Freihat, Shaher Momani

“…The algorithm described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.…”
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