New method for solving system of P.F.D.E. and fractional evolution disturbance equation of distributed order

Some results on the $P_{v,2n}$, $K_{v,n}$, and $H_{v,n}$-integral transforms

“…For example, using a new integral transform, Aghili and Ansari gave a Cauchy type fractional diffusion equation on fractals and expressed its solution in terms of the Laplace type integral in [4]. In addition, generalized integral transforms were used to solve singular integral equations and partial fractional differential equations in [1,2]. Furthermore, the fundamental solutions of the single-order and distributed-order Cauchy type fractional diffusion equations were given using generalized integral transforms in [3].…”

Two unconditionally stable and convergent difference schemes with the extrapolation method for the one‐dimensional distributed‐order differential equations

“…Naber sought the solution of distributed‐order fractional subdiffusion equations by separation of variables and Laplace transform. Aghili and Ansari expressed the solution of fractional evolution disturbance equation of distributed order in term of Wright functions using the L A ‐transform. Mainardi et al investigated the fractional diffusion equation with distributed order between 0 and 1 and provided the Fourier‐Laplace representation of the corresponding fundamental solutions.…”

Exact solutions to some models of distributed-order time fractional diffusion equations via the Fox H functions

“…As a consequence of the above equation by considering the inverse Hankel transform as the Mellin transform convolution (20) and setting…”

“…To change the above relation in the Mellin convolution (20), in a same procedure to pervious section we use the following facts…”