An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

“…In 2015, a new fractional derivative introduced entitled Caputo-Fabrizio and some researchers tried to obtain new techniques for studying of distinct integro-differential equations via the new derivation (see, for example, [14][15][16][17][18][19]) and new fractional models and optimal controls of different phenomena with the non-singular derivative operator (see, for example, [20][21][22][23][24] and [25]). Also, there has been published a lot of work about physical studies on fractional calculus and new aspects of fractional different models with Mittag-Leffler law (see, for example, [26][27][28][29] and [30]).…”

A study of fractional Lotka‐Volterra population model using Haar wavelet and Adams‐Bashforth‐Moulton methods

“…Such models have been extensively studied in the literature. On the other hand, it was shown that in many applications, the use of fractional derivatives provide more realistic models than those obtained via standard derivative (see, eg, previous studies and the references therein). Because of the above reason, the study of fractional models received a great attention form many reserchers.…”

Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain

“…Diffusion equations with fractional order derivatives have been playing more and more important roles. For instance, they appear in mechanics, chemistry, electrical engineering and medicine [1][2][3][4][5][6][7][8][9][10][11]. Time-fractional diffusion equations can be used to describe some anomalous diffusion phenomena in many fields of science [12][13][14][15].…”