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Articles 1 - 7 of 7
Full-Text Articles in Analysis
(R2109) Characterizations Of Tzitzeica Curves Using Conformable Frenet Frame, Aykut Has, Beyhan Yılmaz, Kebire Hilal Ayvacı
(R2109) Characterizations Of Tzitzeica Curves Using Conformable Frenet Frame, Aykut Has, Beyhan Yılmaz, Kebire Hilal Ayvacı
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this study, the conditions for a conformable curve and its spherical indicator curves to be a Tzitzeica curve, will be examined. Thus, by understanding the behavior of the Tzitzeica curve, researchers can gain insight into complex systems and make more accurate predictions about their behavior.
Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak
Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, …
Fractional Difference Operators And Related Boundary Value Problems, Scott C. Gensler
Fractional Difference Operators And Related Boundary Value Problems, Scott C. Gensler
Department of Mathematics: Dissertations, Theses, and Student Research
In this dissertation we develop a fractional difference calculus for functions on a discrete domain. We start by showing that the Taylor monomials, which play a role analagous to that of the power functions in ordinary differential calculus, can be expressed in terms of a family of polynomials which I will refer to as the Pochhammer polynomials. These important functions, the Taylor monomials, were previously described by other scholars primarily in terms of the gamma function. With only this description it is challenging to understand their properties. Describing the Taylor monomials in terms of the Pochhammer polynomials has made it …
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented.
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Applications and Applied Mathematics: An International Journal (AAM)
In this article, modified (G'/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials.
Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar
Generalized Fractional Integral Of The Product Of Two Aleph-Functions, R. K. Saxena, J. Ram, D. Kumar
Applications and Applied Mathematics: An International Journal (AAM)
This paper is devoted to the study and develops the generalized fractional integral operators for a new special function, which is called Aleph-function. The considered generalized fractional integration operators contain the Appell hypergeometric function F3 as a kernel. We establish two results of the product of two Aleph-functions involving Saigo-Maeda operators. On account of the general nature of the Saigo-Maeda operators and the Aleph-function, some results involving Saigo, Riemann-Liouville and Erdélyi-Kober integral operators are obtained as special cases of the main result.
Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu
Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu
Masters Theses & Specialist Projects
This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …