In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demo nstrated by examples MSC: 26A33

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demonstrated by examples MSC: 26A33

We present conditions under which all solutions of the fractional differential equation with the Caputo derivative D ax(t) = f(t, x(t)), a > 1, α ∈ (1, 2), (1) are asymptotic to at+ b as t → ∞ for some real numbers a, b. AMS Classification: 34E10, 34A34

The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graph...

In this article, we consider a fractional differential equation (FDE) with Caputo derivative and study the existence and continuation of its solution. Firstly, we prove a theorem on the existence of local solutions. Then we extend the continuation theorems for ODEs to those FDEs. Also several global existence results for FDE are obtained.

The current study is of interest when performing a useful extension crucial physical problem through non-local singular fractional operator. We provide solutions that include three arbitrary parameters α, ρ, and γ for the Resistance-Capacitance (RC), Inductance-Capacitance (LC), Resistance-Inductance-Capacitance (RLC) electric circuits utilizing generalized type operator in sense Caputo, called...