In this paper we study and design two feed forward neural networks. The first approach uses radial basis function network and second approach uses wavelet basis function network to approximate the mapping from the input to the output space. The trained networks are then used in an conjugate gradient algorithm to estimate the output. These neural networks are then applied to solve differential equation. Results of applying these algorithms to several examples are presented

The aim of this paper is to approximate multidimensional functions by using the type of Feedforward neural networks (FFNNs) which is called Greedy radial basis function neural networks (GRBFNNs). Also, we introduce a modification to the greedy algorithm which is used to train the greedy radial basis function neural networks. An error bound are introduced in Sobolev space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result is published in [16]).

The main objective of this paper is to introduce and study the generality differential operator involving the q-Mittag-Leffler function on certain subclasses of analytic functions.  Also, we  investigate the inclusion properties of these classes, by using the concept of subordination between analytic functions.

      The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics.   

Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studie

In this thesis, we introduce eight types of topologies on a finite digraphs and state the implication between these topologies. Also we studied some pawlak's concepts and generalization rough set theory, we introduce a new types for approximation rough digraphs depending on supra open digraphs. In addition, we present two various standpoints to define generalized membership relations, and state the implication between it, to classify the digraphs and help for measure exactness and roughness of digraphs. On the other hand, we define several kinds of fuzzy digraphs. We also introduce a topological space, which is induced by reflexive graph and tolerance graphs, such that the graph may be infinite. Furthermore, we offered some properties of th

      The topic of modulus of smoothness still gets the interest of many researchers due to its applicable usage in different fields, especially for function approximation. In this paper, we define a new modulus of smoothness of weighted type. The properties of our modulus are studied. These properties can be easily used in different fields, in particular, the functions in the  Besov spaces   when

     In this article, we introduce a two-component generalization for a new generalization type of the short pulse equation was recently found by Hone and his collaborators. The coupled of nonlinear equations is analyzed from the viewpoint of Lie’s method of a continuous group of point transformations. Our results show the symmetries that the system of nonlinear equations can admit, as well as the admitting of the three-dimensional Lie algebra. Moreover, the Lie brackets for the independent vectors field are presented. Similarity reduction for the system is also discussed.