Abstract The article contains the comparative use analysis of fractional derivative three types (Riemann -Liouville, Caputo and model) at Begley -Torvik equation when modeling deformation strength characteristics polymer concrete. We also consider how to obtain a solution initial value problem for model using recurrent kernels sequence. Further, correctness is substantiated establishing type or...

This article introduces a new application of piecewise linear orthogonal triangular functions to solve fractional order differential-algebraic equations. The generalized triangular function operational matrices for approximating Riemann-Liouville fractional order integral in the triangular function (TF) domain are derived. Error analysis is carried out to estimate the upper bound of absolute er...

The paper consider an inhomogeneous creep equation arising from a generalized Voigt model containing Riemann-Liouville fractional derivative of the order 0 < β 1. Laplace transform is used for numerical solution. obtained solutions are compared with experimental data polymer concrete samples. On basis this comparison conclusion about adequacy solution method made, and estimates parameters gi...

In this paper, a time-fractional derivative nonlinear Schrödinger equation involving the Riemann–Liouville fractional is investigated. We first perform Lie symmetry analysis of equation, and then derive reduced equations under admitted optimal-symmetry system. Moreover, with invariant subspace method, several exact solutions for their figures are presented. Finally, new conservation theorem app...

In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving ψ-Riemann–Liouville fractional derivative with nonlocal conditions. We first transformed problem into an integral then analyzed by means Banach fixed-point theorem Krasnoselskiis theorem. Some known results in literature are extended. Finally, example is given to illustrate our theoretical ...

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. We also show that a fractional Brownian motion and the related Riemann–Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of o...

Some new necessary and sufficient conditions for the existence of analytic resolving families operators to linear equation with a distributed Riemann–Liouville derivative in Banach space are established. We study unique solvability natural initial value problem fractional derivatives corresponding inhomogeneous equations. These abstract results applied class boundary problems equations time pol...

Abstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class fractional differential equations by using generalized Riesz operator. One can view results work as refinement existence theory with Riemann–Liouville, Caputo, classical derivative. Some special cases be derived to obtain corresponding equations. We provide an illustrated example unique...

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...

Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann...