In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

The purpose of the matching interdiction problem in a weighted graph is to find two vertices such that the weight of the maximum matching in the graph without these vertices is minimized. An approximate solution for this problem has been presented. In this paper, we consider dendrimers as graphs such that the weights of edges are the bond lengths. We obtain the maximum matching in some types of...

In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...

in this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. the error dynamics of each player depends on its neighbors’ information. detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. the introduced reinforcement learning-based algorithms learn online the approximate solution...

Left and right inverse eigenpairs problem for κ-hermitian matrices and its optimal approximate problem are considered. Based on the special properties of κ-hermitian matrices, the equivalent problem is obtained. Combining a new inner product of matrices, the necessary and sufficient conditions for the solvability of the problem and its general solutions are derived. Furthermore, the optimal app...

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

The problem of cyclic sequence alignment is considered. Most existing optimal methods for comparing cyclic sequences are very time consuming. For applications where these alignments are intensively used, optimal methods are seldom a feasible choice. The alternative to an exact and costly solution is to use a close-to-optimal but cheaper approach. In previous works, we have presented three subop...