Study of a Coupled System with Sub-Strip and Multi-Valued Boundary Conditions via Topological Degree Theory on an Infinite Domain

Abstract

The existence and uniqueness of solutions for a coupled system of Liouville–Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions are investigated in this study. The fractional integro-differential equations contain a finite number of Riemann–Liouville fractional integral and non-integral type nonlinearities, as well as Caputo differential operators of various orders subject to fractional boundary conditions on an infinite interval. At the boundary conditions, we use sub-strip and multi-point contribution. There are various techniques to solve such type of differential equations and one of the most common is known as symmetry analysis. The symmetry analysis has widely been used in problems involving differential equations, although determining the symmetries can be computationally intensive compared to other methods. Therefore, we employ the degree theory due to the Mawhin involving measure of a non-compactness technique to arrive at our desired findings. An interesting pertinent problem has also been provided to demonstrate the applicability of our results.

Novel Exploration of Topological Degree Method for Non-Instantaneous Impulsive Fractional Integro-Differential Equation through Application of Filtering System

“…Remark 3.7 One can observe that the above existence and uniqueness results (see theorems (3.5) and (3.6)) are based on the Ξ− Lipschitz, Ξ− condensing, TDM and Grownwall's inequality. This method is help to prove our result using weaker conditions instead of stronger conditions [3], [4], [8], [9], and [21]. The assumptions (P1)(ii) and (P2)(ii) are satisfied the equation ( 13) then by using the theorems (3.3) and (3.5), we can say the equation ( 13) has a solution on C(ℑ, R n ).…”

“…In recent years, many authors have studied the topological degree method for Caputo fractional differential equations as referred to in the dissertations [3], [4], [5], [8], and [17]. According to this fact, we will prove the TDM of non-instantaneous impulsive fractional integral-differential equations (NIFrIDE) with the Kuratowski measure of a non-compactness operator.…”

Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

“…In recent years, fractional calculus and fractional differential equations (FDEs) can be used to model many nonlocal phenomena in lots of scientific and engineering fields, see [1][2][3][4][5] for examples. However, these nonlocal phenomena are often affected by some stochastic noises.…”

An Existence Study on the Fractional Coupled Nonlinear q -Difference Systems via Quantum Operators along with Ulam–Hyers and Ulam–Hyers–Rassias Stability

“…In recent years, many researchers have studied different branches of this theory and conducted numerous analyses analytically and numerically. Particularly, in recent decades, we can see some papers on the applications of fixed-point theorems to prove the existence of solutions of fractional boundary value problems [1][2][3][4]. Because of the quick developments in fractional calculus, many mathematicians discussed on the theory of q-calculus that is an equivalent of traditional cal-culus without defining the concept of limit, and also the parameter q refers to quantum.…”