In this paper, we propose a numerical method to estimate the unknown order of a Riemann–Liouville fractional derivative for a fractional Stokes’ first problem for a heated generalized second grade fluid. The implicit numerical method is employed to solve the direct problem. For the inverse problem, we first obtain the fractional sensitivity equation by means of the digamma function, and then we...

Some new weakly singular integral inequalities are established by a method, which generalize some results of this type in previous papers. By these inequalities, we present the attractivity solutions for Riemann–Liouville fractional differential equations. Finally, several examples given to illustrate our main results.

In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grünwald–Letnikov derivative, the Riemann–Liouville derivative and the Caputo derivative. Especially, we compare the Riemann–Liouville derivative with the Caputo derivative. And sequential property of the Caputo derivative is also derived, which is helpful in translating the higher fractional-order di...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

<abstract><p>In this paper, we present a general formulation of the well-known fractional drifts Riemann-Liouville type. We state main properties these integral operators. Besides, study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving operators.</p></abstract>