Abstract The integral transform method based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the generalized Weyl space-fractional operator. The solutions, representing ...

In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving generalized Caputo derivative operator supplemented with non-local periodic boundary conditions. We make use fixed point theorems due Banach Krasnoselskii derive desired results. Examples illustrating obtained are also presented.

In the current paper, concept of one-dimensional Shehu Transform have been generalized into three-dimensional namely, Triple (TRHT). Further, some main properties, several theorems and properties related to TRHT established. transform was used in solving fractional partial differential equations, with derivative described Caputo sense. The proposed scheme finds solution without any discretizati...

In this note, we establish the sectorial property of the Caputo fractional derivative operator of order α ∈ (1, 2) with a zero Dirichlet boundary condition.

*Correspondence: [email protected] Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Chang’an Road, Xi’an, China Abstract In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative. The new kernel of Capu...

In the present paper, using novel generalizations of the Hukuhara di¤erence for fuzzy sets, we introduce and study new generalized di¤erentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy di¤erentiabilities …nding connections between them. Characterization and relatively simple expressions are provided f...

In this paper, we investigate the existence and calculation of the expression of periodic solutions for fuzzy differential equations with three types of forcing terms, by using Hukuhara derivative. In particular, Theorems 3.2, 4.2 and 5.2 are the results of existences of periodic solutions for fuzzy differential equations ™,a andb, respectively. These results will help us to study phenomena wit...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...