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...

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 ...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...

Fractional differential equations describe nature adequately because of the symmetry properties that physical and biological processes. In this paper, a new approximation is found for variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on basis, an efficient numerical approach formulated VO time-fractional modified subdiffusion (TFMSDE). Complete theoretical analysis pe...

Fractional differential equations (FDEs) arising in engineering and other sciences describe nature sufficiently terms of symmetry properties. This paper proposes a numerical technique to approximate ordinary fractional initial value problems by applying radial basis function neural network. The derivative used the method is considered Riemann-Liouville type. simple implement approximates soluti...

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...

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

This paper systematically investigates the Lie group analysis method of time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions are obtained. It is shown that governing can be transformed into a ordinary differential new independent variable, where derivatives in Erdèlyi–Kober sense. Furthermore, explicit ana...