It is known that, from a modeling point of view, fractional dynamic equations are more suitable compared to integer derivative models. In fact, equation referred as an with memory. To demonstrate that the model better than corresponding model, we need compute solutions differential and compare them relative data available. this work, will illustrate linear nq-order sequential Caputo equations, ...

This paper is devoted to the existence of solutions for certain classes nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with Dirichlet boundary conditions in Banach spaces. Moreover, our analysis based on Darbo’s fixed point theorem conjunction technique Hausdorff measure noncompactness. An example also presented illustrate effectiveness main results.

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...

‎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...

This paper studies a fractional differential equation combined with Liouville–Caputo operator, namely, LCDηβ,γQ(t)=λϑ(t,Q(t)),t∈[c,d],β,γ∈(0,1],η∈[0,1], where Q(c)=qc is bounded and non-negative initial value. The function ϑ:[c,d]×R→R Lipschitz continuous in the second variable, λ>0 constant operator LCDηβ,γ convex combination of left right derivatives. We study well-posedness using fixed-po...

A reaction-diffusion system can be represented by the Gray-Scott model. In this study, we discuss a one-dimensional time-fractional model with Liouville-Caputo, Caputo-Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional derivatives. We utilize homotopy analysis transformation method to obtain approximate solutions for This gives more realistic series of that converge rapidly exact solution....

Fractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and w...

This paper is concerned with a kind of fractional order systems with Caputo-Hadamard derivative (of order q ∈ C and <(q) ∈ (1, 2)) and not instantaneous impulses. The obtained result uncovers that there exists a general solution for these impulsive systems, which means that the state trajectory of these impulsive systems is non-unique, and it is expounded by a numerical example. c ©2017 All rig...

Email: [email protected] Abstract: In this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equat...