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A Novel Approach for Solving Nonlinear Time Fractional Fisher Partial Differential Equations
Full text linkThis study focuses on solving non-linear time fractional Fisher partial differential equations using analytical series solutions. The authors consider the Caputo fractional derivative in their formulas, which adds accuracy to the results. They introduce a novel method called LRPS which proves to be a powerful tool for obtaining precise analytical and numerical solutions for these equations. The LRPS method emphasizes precision, effectiveness, and practical application, making it suitable for various fields such as physics, engineering, and finance. Due to the importance of accuracy, effectiveness and method of application in this approach, it is highlighted that accurate solutions can be obtained when there is a pattern in the parts of the series, while approximate estimates are provided otherwise. The LRPS method is presented as a powerful technique specifically designed for solving nonlinear fractional Fisher partial differential equations
Use of Mixed Operator Method to a fractional Hadamard Dirichlet boundary value problem
Full text linkThe purpose of this paper is to deal with the following nonlinear Hadamard fractional boundary value problem
HDα1+ u(t) + f(t, u(t), u(t)) + g(t, u(t)) = 0,1 < t < e, 1 < α ≤ 2,u(1) = u(e) = 0,
where HDα 1+ is the Hadamard fractional derivative operator. Using the mixed monotone operator method, we prove an existence and uniqueness result for this mixed fractional Hadamard boundary value problem. As an application of this result, we give one example to establish an existence and uniqueness of a positive solution.
On Sum and Geometric Sum of independent New Quasi Lindley Random Variables and its Applications
Full text linkThe Laplace transformation method is used to drive the distribution of the sum Sn of n-fixed random variables, which has a new quasi Lindley distribution with two parameters θ and α, NQLD (θ,α). The sum of NQLD (SUNQLD) distribution is obtained in pdf and cdf formats. It is discussed how to calculate the random sum SN of a random number of NQLD random variables. The random sum of the NQLD distribution's pdf and cdf are calculated. When N has a geometric distribution, the geometric sum of NQLD distribution (GSN QLD) was introduced as an example of a random number of NQLD random variables. For all cases, some statistical measures are determined. The distribution's parameters are estimated using the maximum likelihood method. To test the viability and efficiency of the proposed distributions SNQLD and GSNQLD, lifetime count data sets from acute myeloid leukaemia are fitted. The results should become accepted knowledge in the fields of probability theory and its allied sciences. In addition, the histogram, fitted probability density function (pdf), and P-P plots for the analyzed real data set are presented
Research of Online and Offline Blended Teaching of College Mathematics
Full text linkThe traditional teaching model faces significant challenges in the era of information technology, while the blended learning model that integrates information technology and educational instruction has become an undeniable trend. Blended learning, which combines online and offline elements, can achieve complementary advantages to a greater extent, effectively enhancing the quality of teaching and promoting students' competence. This article explores the blended learning model, using higher mathematics courses as an example
Quasi Triple Operator on Hilbert Space
No full textIn this pepar we given a newclass of operators onHilbert space calledquasi triple operatorand -Quasi Triple Operator . We study the operator and introdus some properties ofi
Some Statistical Approximation based on Post-Widder operators
Full text linkIn the present paper, we study the convergence of real and modified Post-Widder operators in C, which is known as the extension of approximation of these operators from the real axis in the complex plane. In this direction, we also investigate error estimation in simultaneous approximation and a Voronovskaya-type asymptotic formula. 
Oscillatory Behavior of Higher Order Nonlinear Mixed Type Difference Equations With a Nonlinear Neutral Term
Full text linkThis paper discusses higher order nonlinear neutral mixed type difference equations of the form
Δ^{m}[x(n)+p(n)h(x(σ(n)))]+q(n)f(x(τ(n)))=0, n=0,1,2,…,
where (p(n)), (q(n)) are sequences of nonnegative real numbers, h, f:R→R are continuous and nondecreasing with uh(u)>0, uf(u)>0 for all u≠0, and (σ(n)) and (τ(n)) are sequences of integers such that
lim_{n→∞}τ(n)=lim_{n→∞}σ(n)=∞.
In general, we will examine the oscillatory behavior of the solutions for the above equation. Especially, when m is even, the result obtained here complements studies related to the oscillation of the above equation. In addition, examples showing the accuracy of the results are given
Research and Application of Digital Classroom Teaching Development in the Post-Pandemic Era
Full text linkWith the continuous development of information technology, digital classrooms are becoming more adapted to the demands of talent cultivation in the modern era. The digital classroom teaching model is a reform of traditional teaching methods, and constructing a digital classroom allows for more flexible organization of instructional design, fostering students' creative thinking and enhancing their overall qualities. Seizing the opportunity for the development of applied universities, our school is constructing a locally distinctive path of information technology. This article takes higher mathematics as an example to elaborate on the practical application experience of digital classroom teaching development. In conclusion, this article summarizes the shortcomings in the process of digital classroom construction, which holds certain reference value and significance for future work
Bifurcation analysis of dynamical systems with fractional order differential equations via the modified Riemann-Liouville derivative
Full text linkIn this manuscript, the solutions of linear dynamical systems with fractional differential equations via themodified Riemann-Liouville derivative is derived. By using Jumarie type of derivative (JRL), we stated and provedthe Existence and uniqueness theorems of the dynamical systems with fractional order equations. Also a novel stability analysis of fractional dynamical systems by Jumarie type derivative is established and some important stability conditions are determined. The achieved results have various applications in mathematics, plasma physics and almost all branches of physics that have non-conservative forces. Finally, we investigated interesting application of nonlinear space-time fractional Korteweg-de Vries (STFKdV) equation in Saturn F-ring’s region. Moreover, our investigation could be basic interest to explain and interpret the effects of fractional and modification parameters on STFKdV equation. This is novel study on this model by dynamical system (DS) to describe the behavior of nonlinear waves without solve this system
Problem Oriented Learning and Teaching to Improve the Teaching Quality of Engineering Mathematical Analysis
Full text linkThis paper objectively analyzes the challenges faced by the teaching of engineering mathematical analysis, analyzes the connotation and essence of problem-oriented learning and teaching, puts forward the problem-oriented learning and teaching mode, and tries to improve the teaching quality of engineering mathematical analysis