Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data

On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems

“…Therefore, PDEs with fractional derivatives are a generalization equation with integer-order partial derivatives and a strong theoretical and practical interest. There have been many authors researching this field, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation

“…To cite some recent developments: in 2019 Jajarmi and Baleanu [ 26 ] studied a general form of fractional optimal control problems involving fractional derivative with singular or non-singular kernel; Jothimani et al [ 30 ] discussed an exact controllability of nondensely defined nonlinear fractional integrodifferential equations with the Hille–Yosida operator; Valliammal et al [ 61 ] studied the existence of mild solutions of fractional-order neutral differential system with state-dependent delay in Banach space. In 2020 Jajarmi et al [ 28 ] investigated a fractional version of SIRS model for the HRSV disease; Baleanu et al [ 2 ] proposed a new fractional model for the human liver involving the Caputo–Fabrizio fractional derivative; Baleanu et al [ 3 ] studied the fractional features of a harmonic oscillator with position-dependent mass; Sajjadi et al [ 54 ] discussed the chaos control and synchronization of a hyperchaotic model in both the frameworks of classical and of fractional calculus; Jajarmi and Baleanu [ 27 ] proposed a new iterative method to generate the approximate solution of nonlinear fractional boundary value problems in the form of uniformly convergent series; Shiri et al [ 56 ] employed discretized collocation methods for a class of tempered fractional differential equations with terminal value problems; Tuan et al [ 60 ] tackled the problem of finding the solution of a multi-dimensional time-fractional reaction-diffusion equation with nonlinear source from the final value data; Li et al [ 44 ] proposed a new approximation for the generalized Caputo fractional derivative based on WSGL formula and solved a generalized fractional sub-diffusion problem; Gao et al [ 19 ] studied the epidemic predictability for the novel coronavirus (2019-nCoV) pandemic by analyzing a time-fractional model and finding its solution by a q -homotopy analysis transform method; Gao et al [ 20 ] investigated the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense; Gao et al [ 21 ] tackled the fractional Phi-four equation by using a q -homotopy analysis transform method numerically; Sabir et al [ 53 ] presented a novel meta-heuristic computing solver for solving the singular three-point second-order boundary value problems using artificial neural networks.…”

On a Kirchhoff diffusion equation with integral condition

“…Pulkina et al [15], and in the references therein. Besides, there are many works which focused on this topic; see, e.g., [16][17][18][19][20][21][22][23][24][25][26][27].…”