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 work, we perform univariate approximation with rates, basic and fractional, of continuous functions that take values into an arbitrary Banach space domain on a closed interval or all reals, by quasi-interpolation neural network operators. These approximations are achieved deriving Jackson-type inequalities via the first modulus continuity hand function its abstract integer derivative Ca...

In this paper we establish the existence, uniqueness and regularity of heat kernels to a large class time-inhomogeneous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates, gradient fractional derivative are obtained.

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

Fractional integrals and inequalities have recently become quite popular been the prime consideration for many studies. The results of different types studied by launching innovative analytical techniques applications. These Hermite–Hadamard are discovered in this study using Atangana–Baleanu integral operators, which provide both practical powerful results. In paper, a symmetric type is provid...

Abstract We study the optimal feedback control for fractional evolution equations with a nonlinear perturbation of time-fractional derivative term involving Caputo derivatives arbitrary kernels. Firstly, we derive mild solution in terms semigroup operator generated by resolvents and kernel from general operators establish existence uniqueness solutions systems. Then, feasible pairs applying Fil...

In this paper, we study a new operational numerical method for hybrid fuzzy fractional differential equations by using of the hybrid functions under generalized Caputo- type fuzzy fractional derivative. Solving two examples of hybrid fuzzy fractional differential equations illustrate the method.

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

The separation of wave modes from isotropic elastic wavefields is typically done using Helmholtz decomposition. However, Helmholtz decomposition using conventional divergence and curl operators in anisotropic media does not give satisfactory results and leaves the different wave modes only partially separated. The separation of anisotropic wavefields requires the use of more sophisticated opera...

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...