In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step ...sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in
p
-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods.
In this work, we introduce two Bregman projection algorithms with self-adaptive stepsize for solving pseudo-monotone variational inequality problem in a Hilbert space. The weak and strong convergence ...theorems are established without the prior knowledge of Lipschitz constant of the cost operator. The convergence behavior of the proposed algorithms with various functions of the Bregman distance are presented. More so, the performance and efficiency of our methods are compared to other related methods in the literature.
This paper presents the nonlinear systems of Volterra-type fractional integro-differential equation solutions through a Chebyshev pseudospectral method. The proposed method is based on the Caputo ...fractional derivative. The results that we get show the accuracy and reliability of the present method. Different nonlinear systems have been solved; the solutions that we get are compared with other methods and the exact solution. Also, from the presented figures, it is easy to conclude that the CPM error converges quickly as compared to other methods. Comparing the exact solution and other techniques reveals that the Chebyshev pseudospectral method has a higher degree of accuracy and converges quickly towards the exact solution. Moreover, it is easy to implement the suggested method for solving fractional-order linear and nonlinear physical problems related to science and engineering.
In this paper, we introduce two algorithms for finding a common solution of the monotone inclusion problem and the fixed point problem for a relatively nonexpansive mapping in reflexive Banach ...spaces. The weak convergence results for both algorithms are established without the prior knowledge of the Lipschitz constant of the mapping. An application to the variational inequality problem is considered. Finally, some numerical experiments of the proposed algorithms including comparisons with other algorithms are provided.
In this paper, we study the multiple-sets split common null point problem (MSCNPP) in Banach spaces. We introduce a new self-adaptive algorithm for solving this problem. Under suitable conditions, we ...prove a strong convergence theorem of the proposed algorithm. An application of the main theorem to the multiple-sets split feasibility problem in Banach spaces is also presented. Finally, we provide the numerical experiments which show the efficiency and implementation of the proposed method.
In this article, we also introduced two well-known computational techniques for solving the time-fractional Fornberg–Whitham equations. The methods suggested are the modified form of the variational ...iteration and Adomian decomposition techniques by ρ-Laplace. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available methods. The graphical representation of the exact and derived results is presented to show the suggested approaches reliability. The comparative solution analysis via graphs also represented the higher reliability and accuracy of the current techniques.
Motivated by the importance of diffusion equations in many physical situations in general and in plasma physics in particular, therefore, in this study, we try to find some novel solutions to ...fractional-order diffusion equations to explain many of the ambiguities about the phenomena in plasma physics and many other fields. In this article, we implement two well-known analytical methods for the solution of diffusion equations. We suggest the modified form of homotopy perturbation method and Adomian decomposition methods using Jafari-Yang transform. Furthermore, illustrative examples are introduced to show the accuracy of the proposed methods. It is observed that the proposed method solution has the desire rate of convergence toward the exact solution. The suggested method’s main advantage is less number of calculations. The proposed methods give series form solution which converges quickly towards the exact solution. To show the reliability of the proposed method, we present some graphical representations of the exact and analytical results, which are in strong agreement with each other. The results we showed through graphs and tables for different fractional-order confirm that the results converge towards exact solution as the fractional-order tends towards integer-order. Moreover, it can solve physical problems having fractional order in different areas of applied sciences. Also, the proposed method helps many plasma physicists in modeling several nonlinear structures such as solitons, shocks, and rogue waves in different plasma systems.
Applying the electric field to a fluid flowing on an infinite vertical plate is the most recent technique used for studying fluid movement. This technique is known as electro-osmotic flow (EOF). ...Therefore, the core aim of the present research work is to examine the time-dependent electro-osmotic flow of viscoelastic fluid on a vertical flat plate together with the effects of heat generation and chemical reaction. The classical system of governing equations has been fractionalised by means of Caputo–Fabrizio’s time-fractional derivative. Governing equations have been non-dimensionalised by using relative dimensionless quantities. The exact solutions for the momentum, temperature and concentration equations have been developed by implementing the Laplace transform technique. For graphical analysis, the solutions have been plotted against the inserted parameters using the computational software Mathematica. It is interesting to mention that the time-fractional model provides more than one fluid layer for the analysis of the fluid motion, heat distribution and mass concentration, which is not possible by assuming the classical mathematical model. It is also very important to mention that the velocity profile shows declination for greater values of electro-osmotic parameter
Es
.
The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in ...reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed methods. The results presented in this paper improve and generalize many known results in recent literature.
In this work, we introduce two modified Tseng's splitting algorithms with a new non-monotone adaptive step size for solving monotone inclusion problem in the framework of Banach spaces. Under some ...mild assumptions, we establish the weak and strong convergence results of the proposed algorithms. Moreover, we also apply our results to variational inequality problem, convex minimization problem and signal recovery, and provide several numerical experiments including comparisons with other related algorithms.
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