Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity

Existence and Stability for a Nonlinear Coupledp-Laplacian System of Fractional Differential Equations

“…Lemma 3 (see [2,8]). Let ϱ ∈ (n − 1, n], Z ∈ C n− 1 , and R D ϱ is the fractional derivative for Riemman-Liouville, then (12) for b i ∈R and i � 1, 2, 3, 4, .…”

“…e theoretical development of fractional calculus and its applications is more important to model nonlinear complex problems with the arbitrary fractional order. e subject of fractional differential equations (FDEs) has become an important area in real life because of their ability to model a lot of physical phenomena associated with rapid and concise changes with their significance in science and engineering through the past three decades, such as chemistry, physics, biology, engineering, visco-elasticity, electrotechnical, signal processing, electrochemistry, and controllability (see the details, [1][2][3][4][5][6][7][8][9], and the reference therein). In the near time, the nonlinear fractional partial differential equations are the most applied research area in which most authors and scientists are focused for their investigation.…”

“…where ϱ i , θ i ∈ (1, 2] and δ i , η i ∈ (0, 1], for i � 1 and 2. e study of positive solutions to boundary value problems for fractional-order differential equations using the topological degree theory technique is rarely available in the literature, so this research field needs further elaboration. Most papers that dealt the topological degree theory with fractional orders belong to (0, 1) or (1,2]. For the uniqueness and existence analysis of nonlinear fractional differential equations, the case only Caputo fractional derivative is used frequently.…”

Existence and Stability of the Solution to a Coupled System of Fractional-order Differential with a $p$-Laplacian Operator under Boundary Conditions

“…Therefore, fractional calculus is the generalization of classical calculus. For information about applications of fractional equations, we suggest to the readers see these papers ( [1,2,3,4,5,6,7,8,9,10,53]). Fractional calculus has got the attention of researchers in the various applied sciences due to the important applications, high profile accuracy, and usability in the different fields like image processing, fractals theory, control system, electromagnetic theorem, control theory ecology, metallurgy, plasma physics, aerodynamics, economics, and biology.…”

Numerical study on factional differential-algebraic systems by means of Chebyshev Pseudo spectral method

“…Nowadays, the fractional differential equations (FDEs) have gained increased appearances in varied problems in various fields of physics, chemistry, biology, applied science and engineering, this is due to their accuracy in modelling these problems [1][2][3][4][5][6][7][8]. Consequently, the development of analytical and numerical algorithms for FDEs is an interested topic for many researches [9][10][11][12][13][14][15][16].…”