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...

Physical phenomena and natural disasters, such as tsunamis floods, are caused due to dispersive water waves shallow by earthquakes. In order analyze minimize damaging effects of situations, mathematical models presented different researchers. The Wu–Zhang (WZ) system is one model that describes long waves. this regard, the current study focuses on a non-linear (2 + 1)-dimensional time-fractiona...

Abstract The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with singular Caputo kernel and nonsingular Caputo–Fabrizio Atangana–Baleanu (ABC) kernel. proposed method based on the discrete Temimi–Ansari method, which combined three different schemes that are appropriate new derivative operators. technique used ...

‎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...

in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

In the current study, blood flow through an inclined cylindrical tube subjected to external magnetic field is evaluated. The has been considered under consequence of a transverse field. Previously mathematical model was solved by using Caputo-Fabrizio (CF) fractional order derivative with non-singular kernel which limitations like it fails satisfy fundamental theorem calculus. Whereas, in prese...