In this paper, the time-fractional Fisher’s equation (TFFE) is considered to exam the analytical solution using the Laplace q-Homotopy analysis method (Lq-HAM)â€. The Lq-HAM is a combined form of q-homotopy analysis method (q-HAM) and Laplace transform. The aim of utilizing the Laplace transform is to outdo the shortage that is mainly caused by unfulfilled conditions in the other analytical methods. The results show that the analytical solution converges very rapidly to the exact solution.
In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation. The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation
A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon is mostly rising in electromagnetic influences and production of electric signals. The proposed technique called as He-Fractional Laplace technique with help of Homotopy perturbation is utilized to found the exact and nearly approximated results of differential model and numerical example of telegraph equation or damped wave equation in this article. The most unique term of this technique is that, there is no worry to find the next iteration by integration in recurrence relation. As fractional Laplace integral transformation has some limitations in non-linear terms, to get the result of nonlinear term in
... Show MoreTransformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s Polynomials is provided as the transformation plays an essential role in solving differential linear and non-linear equations. Here is the α-Sumudu technique to find the relevant results of the gas dynamics equation in fractional order. To calculate the non-linear fractional gas dynamical problem, a consumer method created on the new homotopy perturbation a-Sumudu transformation method (HP TM) is suggested. In the Caputo type, the derivative is evaluated. a-Sumudu homotopy pe
... Show MoreBackground: Malignant lymphoma is a term that describes primary tumors of the lymphoreticular system, almost all of which arise from lymphocytes.MMP-1 is the most ubiquitously expressed interstitial collagenase, a subfamily of MMPs that cleaves stromal collagens. It is also called collagenase-1.TIMPs which inhibits MMP activity and thereby restrict extracellular matrix breakdown, TIMP-1 is a stromal factor that has a wide spectrum of functions in different tissues. Material and Methods: This study was performed on (68) formalin-fixed, paraffin-embedded blocks, histopathologically diagnosed as lymphoma (head and neck lesions). Immunohistochemical staining of MMP1and TIMP1 was performed on each case of the study sample. Results: The expressio
... Show MoreThis paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear time-fractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations.
Neuroimaging is a description, whether in two-dimensions (2D) or three-dimensions (3D), of the structure and functions of the brain. Neuroimaging provides a valuable diagnostic tool, in which a limited approach is used to create images of the focal sensory system by medicine professionals. For the clinical diagnosis of patients with Alzheimer's Disease (AD) or Mild Cognitive Impairs (MCI), the accurate identification of patients from normal control persons (NCs) is critical. Recently, numerous researches have been undertaken on the identification of AD based on neuroimaging data, including images with radiographs and algorithms for master learning. In the previous decade, these techniques were also used slowly to differentiate AD a
... Show MoreThis work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.
In this paper, Min-Max composition fuzzy relation equation are studied. This study is a generalization of the works of Ohsato and Sekigushi. The conditions for the existence of solutions are studied, then the resolution of equations is discussed.