In this paper, we introduce the definition of a new general Integral transform which call it "A new general polynomial transform ". Also, we introduce properties, theorems, proofs and transforms of the Logarithmic functions, polynomials functions and other functions. As well as, we discuss how we can apply this Integral transform and its inverse to solve the ordinary differential equations with variable coefficients.

In this paper, a new approach to the numerical solution of Volterra-Fredholm Integral equations by using expansion method based on the composition of the inverse and direct discrete fuzzy transforms (shortly F-transforms) in combination with the collocation technique is proposed. First, the unknown function is approximated by using the composition of the inverse and direct discrete F-transforms based on the fuzzy partition, then the Volterra-Fredholm Integral equation is reduced to the linear system of equations. Moreover, the convergence theorem for the proposed method is given in terms of the modulus of continuity. Finally, illustrative examples are included to show the accuracy and the efficiency of the proposed method.

In this paper we shall examine the quadratic Fourier transform which is introduced by the generalized quadratic function for one order parameter in the ordinary Fourier transform. This will be done by analyzing corresponding six subcases of the quadratic Fourier transform within a reproducing kernel Hilbert spaces framework.

This work aims to study F-transforms based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of F-transforms fail to hold in the case of implicators, such as S-and QL-implicators. Further, we establish an equivalence between L-fuzzy transformation systems and F-transforms.

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients.