using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

In this paper, we investigated the sharp estimate for condition of given interval which guarantees unique solution a Reimman-Liouville-type fractional differential equations with boundary conditions. The method analysis is obtained by principle contraction mapping through using maximum value integral Green?s function. Besides, also concluded sharper lower bound eigenvalues an eigenvalue problem...

In this research, we establish some new fixed-point results for a symmetric coupled dominated fuzzy mapping satisfying advanced contraction on closed ball in the setting of complete metric spaces. addition, notion hybrid fuzzy-graph-dominated mappings introduced spaces achieves problems. Some definitions and illustrative examples are given to validate our findings. Lastly, demonstrate originali...

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. particular, generalized existing results a pair of mappings that possess but not continuous at point. We can apply result both discontinuous mappings. concluded our by providing an illustrative example each case application to existence uniqueness solution nonlinear Volterra i...

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under conditions spaces with illustrative examples support our results. will play a very important role theory and can be generalized for different contractive context Moreover, we present an application nonlinear integral equation get existing resul...

Motivated by the famous Waddington's epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to construct the landscape for multi-stable complex systems. We aim to summarize and elucidate the relationships among these theories from a mathematical point of view. We systematically investigate and compare three different but closely...