Reconsideration of the Ordinary Derivative Xk Variation

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

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A variety of wave amplitudes for the conformable fractional (2 + 1)-dimensional Ito equation

Modern Physics Letters B ◽

10.1142/s0217984921502547 ◽

2021 ◽

pp. 2150254

Author(s):

Emad A. Az-Zo’bi ◽

Wael A. Alzoubi ◽

Lanre Akinyemi ◽

Mehmet Şenol ◽

Basem S. Masaedeh

Keyword(s):

Mapping Method ◽

Jacobi Elliptic Function ◽

Conformable Derivative ◽

Hyperbolic Functions ◽

Fractional Complex Transform ◽

New Exact Solutions ◽

Higher Dimensional ◽

Fractional Orders ◽

Ito Equation ◽

Ordinary Derivative

The conformable derivative and adequate fractional complex transform are implemented to discuss the fractional higher-dimensional Ito equation analytically. The Jacobi elliptic function method and Riccati equation mapping method are successfully used for this purpose. New exact solutions in terms of linear, rational, periodic and hyperbolic functions for the wave amplitude are derived. The obtained solutions are entirely new and can be considered as a generalization of the existing results in the ordinary derivative case. Numerical simulations of some obtained solutions with special choices of free constants and various fractional orders are displayed.

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Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields

Journal of High Energy Physics ◽

10.1007/jhep06(2012)062 ◽

2012 ◽

Vol 2012 (6) ◽

Cited By ~ 25

Author(s):

R. R. Metsaev

Keyword(s):

Arbitrary Spin ◽

Ordinary Derivative

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On The K-Pseudo Symmetric and Ordinary Differentiation

Demonstratio Mathematica ◽

10.1515/dema-2016-0014 ◽

2016 ◽

Vol 49 (2) ◽

Author(s):

E. Łazarow ◽

M. Turowska

Keyword(s):

Continuous Function ◽

Lebesgue Measure ◽

Measure Zero ◽

Lebesgue Measure Zero ◽

Definition Of ◽

Ordinary Derivative ◽

Symmetric Derivative

AbstractIn 1972, S. Valenti introduced the definition of k-pseudo symmetric derivative and has shown that the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is of Lebesgue measure zero. In 1993, L. Zajícek has shown that for a continuous function f, the set of all points, at which f is symmetrically differentiable but no differentiable, is σ-(1 - ε) symmetrically porous for every ε > 0. The question arises: can we transferred the Zajícek’s result to the case of the k-pseudo symmetric derivative?In this paper, we shall show that for each 0 < ε < 1 the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is σ-(1 - ε)-porous.

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ERRATA: The Symmetric and Ordinary Derivative

Real Analysis Exchange ◽

10.2307/44151138 ◽

1977 ◽

Vol 3 (2) ◽

pp. 109

Keyword(s):

Ordinary Derivative

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20. The derivative claim and the rule in Foss v Harbottle

10.1093/he/9780198848493.003.0020 ◽

2021 ◽

pp. 467-494

Author(s):

Brenda Hannigan

Keyword(s):

Supreme Court ◽

Common Law ◽

Current Position ◽

Important Constraint ◽

The Supreme Court ◽

The Common ◽

Breach Of Duty ◽

Ordinary Derivative

This chapter discusses further aspects of shareholder remedies, namely the common law multiple derivative claim; derivative claims under Companies Act 2006 (CA 2006), Part 11; the reflective loss principle; personal actions at common law; and specific statutory rights under the CA 2006. At common law, a shareholder aggrieved by a breach of duty by a director could bring a derivative claim on behalf of the company, as an exception to the rule in Foss v Harbottle. That common law claim now remains as a common law multiple derivative claim whereas the ‘ordinary’ derivative claim now is a statutory claim under CA 2006, Part 11. This chapter explores both types of derivative claim and assesses their value to shareholders. An important constraint on shareholder recovery is the principle governing reflective loss which has recently been restated by the Supreme Court. This chapter considers the current position in the light of that development.

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Radiotherapy cancer treatment modeling with fractional or ordinary derivative

Journal of Cancer Science and Therapeutics ◽

10.36879/jcst.19.000114 ◽

2019 ◽

pp. 1-3

Keyword(s):

Fractional Derivative ◽

Cancer Treatment ◽

Treatment Process ◽

Short Communication ◽

Tumor Volume ◽

Treatment Model ◽

Normal Cells ◽

Initial Tumor ◽

Ordinary Derivative ◽

Radiotherapy Treatment

This short communication presents two versions of the cancer treatment model, the ordinary derivative version and the fractional derivative version. The two models were used to simulate a cancer treatment process of a cancer patient with an initial tumor volume of 28.4 cm3 . The simulated final volumes produced by the fractional derivative version were 28.17 cm3 and 5.68 cm3 the normal cells and tumor respectively, while those of the ordinary derivative version were 16.97 cm3 and 0.0 cm3 . In addition, the fractional derivative version was used to simulate a no-treatment process with an initial tumor volume of 5 cm3 , and the final volumes were 4.91 cm3 and 17.41 cm3 for the normal cells and tumor respectively. It was concluded that the radiotherapy treatment process was better simulated with the fractional derivative model.

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New Symmetric Differential and Integral Operators Defined in the Complex Domain

Symmetry ◽

10.3390/sym11070906 ◽

2019 ◽

Vol 11 (7) ◽

pp. 906 ◽

Cited By ~ 3

Author(s):

Rabha W. Ibrahim ◽

Maslina Darus

Keyword(s):

Differential Operator ◽

Unit Disk ◽

Function Theory ◽

Open Unit ◽

Open Unit Disk ◽

Geometric Function ◽

Ruscheweyh Derivative ◽

Symmetry Properties ◽

Statistical Studies ◽

Ordinary Derivative

The symmetric differential operator is a generalization operating of the well-known ordinary derivative. These operators have advantages in boundary value problems, statistical studies and spectral theory. In this effort, we introduce a new symmetric differential operator (SDO) and its integral in the open unit disk. This operator is a generalization of the Sàlàgean differential operator. Our study is based on geometric function theory and its applications in the open unit disk. We formulate new classes of analytic functions using SDO depending on the symmetry properties. Moreover, we define a linear combination operator containing SDO and the Ruscheweyh derivative. We illustrate some inclusion properties and other inequalities involving SDO and its integral.

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Explicit Solutions of Initial Value Problems for Linear Scalar Riemann-Liouville Fractional Differential Equations With a Constant Delay

Mathematics ◽

10.3390/math8010032 ◽

2019 ◽

Vol 8 (1) ◽

pp. 32 ◽

Cited By ~ 2

Author(s):

Ravi Agarwal ◽

Snezhana Hristova ◽

Donal O’Regan

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Initial Value Problems ◽

Initial Condition ◽

Constant Delay ◽

Initial Value ◽

Fractional Differential ◽

Set Up ◽

Ordinary Derivative ◽

Linear Scalar

In this paper, we study Linear Riemann-Liouville fractional differential equations with a constant delay. The initial condition is set up similarly to the case of ordinary derivative. Explicit formulas for the solutions are obtained for various initial functions.

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