‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

In this work, we consider the multidimensional time-fractional diffusion equation with $$\psi $$ -Hilfer derivative. This fractional derivative enables interpolation between Riemann–Liouville and Caputo derivatives its kernel depends on an arbitrary positive monotone increasing function ,$$ thus encompassing several in literature. allows us to obtain general results for different families of pr...

Abstract Arc magmatism is fundamental to the generation of new continental or island arc crust. However, mechanisms that add chemical complexity natural calc-alkaline magmas ranging from basaltic rhyolitic compositions are debated. Differentiation currently discussed include magma mixing, assimilation, crustal melting, (fractional) crystallisation. In this contribution, differentiation by decom...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

In this paper, in the class of smooth functions, integration and differentiation operators connected with fractional conformable derivatives are introduced. The mutual reversibility these is proved, properties functions studied. Using transformations generalizing involutive transformations, a nonlocal analogue Laplace operator For corresponding Poisson equation, solvability some boundary value ...

In this paper, design of linear phase FIR digital differentiators is investigated using convex optimization. The problem of differentiator design is first described in terms of convex optimization with different optimization variables’ options, taken one at a time. The method is then used to design first order low pass differentiators and results are compared with Salesnick’s technique and Park...

The main objective of this paper is to estimate the whole set of feasible parameters of a fractional differentiation model, based on gain and phase frequency data. All parameters, including differentiation orders, are expressed as intervals and then estimated using a bounded error approach. A contraction method named forward-backward propagation is first applied to reduce the initial searching ...