the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

The fractional calculus, an active branch of mathematical analysis, is as old as the classical calculus which we know today. In recent years, fractional differential equations have been studied by many researchers, ranging from the theoretical aspects of existence and uniqueness to the numerical methods for finding solutions. It is well known that fractional differential equations provide an ex...

This paper is concerned with the finite-time stability of -Hilfer type fuzzy fractional differential equations (FFDEs) time delay. By applying standard theorems and a hypothetical condition, we explore existence solution stabilty results.

The main purpose of this paper was to consider new sandwich pairs and investigate the existence a solution for class fractional differential equations with p-Laplacian via variational methods in ψ-fractional space Hpα,β;ψ(Ω). results obtained are first make use theory ψ-Hilfer operators p-Laplacian.

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...