Power Series Solution of Time-Fractional Majda-Biello System Using Lie Group Analysis

Theoretical and spectral numerical study for fractional Van der Pol equation

“…Many researchers in different branches of physics, mathematics, and engineering are interested in studying fractional calculus due to its many real-life applications, such as ultrasonic wave propagation, 1 optimal control, 2,3 viscoelastic behavior modeling, 4 linear viscoelasticity, 5 variational problems, 6 fluid mechanics, 7 and other applications have been presented in previous studies. [8][9][10][11][12][13] Searching for numerical techniques to solve fractional differential equations has been strongly considered over the last few decades, some of these methods are the fractional finite volume method, 14 spectral collocation method, 15 random variable transformation technique, 16 operational matrix method, 17 Adomian decomposition method, 18 power series method, 19 nonpolynomial spline method, 20 Gauss-collocation method, 21 radial basis functions method, 22 modified Galerkin algorithm, 23 and other methods have been introduced; see previous studies. [24][25][26][27][28][29][30][31] The tau approach is considered as one of the highly accurate methods that have been used for different kinds of fractional differential equations.…”

Computation of certain integral formulas involving generalized Wright function

“…In this section, considering the integral in (15) and the generalized Wright function in (2), we establish two theorems as follows.…”

“…The research on integral transforms involving special functions (see, e.g., [1-4, 6, 8-12, 19]) has received a considerable attention of the research community primarily because their application has made prominent contributions in several domains of mathematics, engineering and their applications in mathematical physics (see, e.g., [7,15,21,22,[27][28][29][30]). Among these special functions of mathematical physics, the Wright, the Bessel, and similar functions are of central importance and are fairly useful in the theory of integral and fractional calculus.…”

The exponential behavior of 3D stochastic primitive equations driven by fractional noise

“…In several studies, 6‐8 fractional derivative is considered in Atangana–Baleanu sense for studying different models, and numerical results are also demonstrated to support the outcomes of the studies. Local fractional derivative studies and relevant computational method discussions are given in Singh et al 9,10 In several studies, 11‐13 various time‐fractional differential systems are studied and applied to model real‐world phenomena.…”