An Infinite System of Fractional Order with p-Laplacian Operator in a Tempered Sequence Space via Measure of Noncompactness Technique

Abstract

In the current study, a new class of an infinite system of two distinct fractional orders with p-Laplacian operator is presented. Our mathematical model is introduced with the Caputo–Katugampola fractional derivative which is considered a generalization to the Caputo and Hadamard fractional derivatives. In a new sequence space associated with a tempered sequence and the sequence space c0 (the space of convergent sequences to zero), a suitable new Hausdorff measure of noncompactness form is provided. This formula is applied to discuss the existence of a solution to our infinite system through applying Darbo’s theorem which extends both the classical Banach contraction principle and the Schauder fixed point theorem.

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian

“…According to (H4) and ( 13), we know that (a4) in Lemma 3 holds. Similar to (11), noticing that log t s α+β−1 and 1 s are monotonically decreasing with respect to s in [1, e], we have…”

“…In [4], based on the Guo-Krasnosel'skii fixed point theorem, the authors probed into the multiple positive solutions of a system of mixed Hadamard fractional BVP with (p 1 , p 2 )-Laplacian. In fact, some articles have been disposed of the BVP of p-Laplacian system involving Riemann-Liouville or Caputo fractional derivatives (see [5][6][7][8][9][10][11][12][13]).…”

“…In addition, we build the generalized Ulam-Hyers stability of system (1) based on nonlinear analysis methods and inequality techniques. (c) Many previous papers (see [2][3][4][5][6][7][8][9][10][11][12][13][17][18][19]24,25]) usually used some fixed-point theorems on Banach spaces to study the existence of solutions of fractional differential equations. However, we handle the existence of solutions to fractional order differential equations by defining two different distances on a complete distance space.…”

On Coupled System of Langevin Fractional Problems with Different Orders of μ-Caputo Fractional Derivatives

“…Otherwise, the extended Langevin equation represents the particle motion (see, e.g., [11,12]). In fractal media, Langevin's equation has become widely used to represent dynamical operations (see [13][14][15][16][17][18] for more recent interesting results). In [19], the authors utilized the fractional Langevin equation to recreate Brownian motion.…”

Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

“…The phrase time-delay can be used to explain the history of a previous condition. Time-delay has applications in biology, control theory, engineering, population dynamics, physics, and other fields [14][15][16][17][18][19][20][21][22]. As a result, information regarding fractional differential delay equations have disseminated through research and investigations.…”