Existence and discrete approximation for optimization problems governed by fractional differential equations

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

“…Fractional calculus is a generalization for derivatives and integrals of integer order. This mathematical representation has successfully been utilized to describe several problems in engineering practices [1][2][3][4][5][6][7]. In the literature, there are many definitions of fractional derivative, the most popular definitions are of Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio, Atangana-Baleanu, Riesz, Hilfer, among others [8][9][10].…”

A solution for fractional PDE constrained optimization problems using reduced basis method

“…Zacky and Mchado Zaky and Machado (2017) provided a solution for FODCP by pseudo-spectral method. As well as there exist variety of solutions for various fractional optimal control problems that the some of them can be seen in Bai et al (2018); Salati et al (2018).…”

Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance

“…In recent years, the discussion of fractional initial value problems (IVPs) and BVPs have attracted the attention of many scholars and valuable results have been obtained (see ). Various methods have been utilized to study fractional IVPs and BVPs such as the Banach contraction map principle (see [8][9][10][11]), fixed point theorems (see [12][13][14][15][16][17][18]), monotone iterative method (see [19][20][21]), variational method (see [22][23][24]), fixed point index theory (see [17][18][19][20][21][22][23][24][25]), coincidence degree theory (see [26][27][28][29]), and numerical methods [30,31]. For instance, Jiang (see [26]) studied the existence of solutions using coincidence degree theory for the following fractional BVP:…”