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 ...

A fractional time derivative is introduced into Burger’s equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equation...

in this work, we have applied elzaki transform and he's homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he's homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he's homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...

In this paper we introduce the notion of α-martingale as the fractional derivative of order α of a continuous local martingale, where α ∈ (−12 , 1 2), and we show that it has a nonzero finite variation of order 2 1+2α , under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Lévy’s characterization theorem for the f...

<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version SIR epidemic mathematical model by means non-local non-singular ABC derivative operator with complete memory effects. Existence uniqueness solution for proposed proved. an optimal control also established. Then, necessary optimality conditions are derived. As conse...

Abstract This research inscription gets to grips with two novel varieties of boundary value problems. One them is a hybrid Langevin fractional differential equation, whilst the other coupled system equation encapsuling collective derivative known as ψ -Caputo operator. Such operators are generated by iterating local integral function respect another increasing positive Ψ. The existence solution...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

Fractional Langevin equation to describe anomalous diffusion. Abstract A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional ...

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to il...