Recently, a new fractional derivative operator has been introduced so that it presents the combination of Riemann–Liouville integral and Caputo derivative. This paper aims to enhance reproducing kernel Hilbert space method (RKHSM, for short) solving certain differential equations involving this is first time application RKHSM employed some with operator. We illustrate convergence analysis appli...

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.

Our main goal in this paper is to investigate the regularity of mild solution fractional diffusion equation which can be used modelling heat transfer with memory effects. Under some various assumptions input data, we obtain two results. We also provide upper bound and lower source function. The tool use complex evaluations involving Wright

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined mountain pass theorem, prove that such has nontrivial weak solution. Our main result significantly complement improves previous papers in literature.

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...