Current Issue : October-December Volume : 2023 Issue Number : 4 Articles : 5 Articles
Adomian decomposition is a semi-analytical approach to solving ordinary and partial differential equations. This study aims to apply the Adomian Decomposition Technique to obtain analytic solutions for linear and nonlinear time-fractional Klein-Gordon equations. The fractional derivatives are computed according to Caputo. Examples are provided. The findings show the explicitness, efficacy, and correctness of the used approach. Approximate solutions acquired by the decomposition method have been numerically assessed, given in the form of graphs and tables, and then these answers are compared with the actual solutions. The Adomian decomposition approach, which was used in this study, is a widely used and convergent method for the solutions of linear and non-linear time fractional Klein-Gordon equation....
All elements in the cyclic group C(n) = {g0 (= e), g, g2 ,, gn−1} are generated by a generator g . The number of generators of gi ,i∈S (n) of C(n) , namely S (n) is known to be Euler’s totient function ϕ (n) ; however, the average probability of an element being a generator has not been discussed before. Several analytic properties of ϕ (n) have been investigated for a long time. However, it seems that some issues still remain unresolved. In this study, we derive the average probability of an element being a generator using previous classical studies....
In this paper, generalized R′-implications are introduced and studied. Although they are not always fuzzy implications, the sufficient and necessary condition such that a generalized R′-operation is a fuzzy implication is discovered and proved. The satisfaction or violation of some basic properties of fuzzy implications, such as the left neutrality property, the identity principle, and the left ordering property, is also investigated and presented. The intersections among the classes of generalized R′-implications (respectively, operations), R-implications, and R′-implications (respectively, operations) are also studied. It is demonstrated that the generalized R′-implications class is a hyper class of the known R- and R′-implications classes. This research also completes the investigation into R′-operations and improves the outcomes of the intersection of R- and R′-implications....
We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman....
The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution....
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