Existence and uniqueness of solutions for coupled systems of Liouville-Caputo type fractional integrodifferential equations with Erdélyi-Kober integral conditions

Abstract

In this paper, we examine a coupled system of fractional integrodifferential equations of Liouville-Caputo form with nonlinearities depending on the unknown functions, as well as their lower-order fractional derivatives and integrals supplemented with coupled nonlocal and Erdélyi-Kober fractional integral boundary conditions. We explain that the topic discussed in this context is new and gives more analysis into the research of coupled boundary value problems. We have two results: the first is the existence result of the given problem by using the Leray-Schauder alternative, whereas the second referring to the uniqueness result is derived by Banach’s fixed-point theorem. Sufficient examples were also supplemented to substantiate the proof, and some variations of the problem were discussed.

Integro-differential equations implicated with Caputo-Hadamard derivatives under nonlocal boundary constraints

“…The boundary value problem (BVP) has been a pivotal component in the development of classical calculus in recent times. Furthermore, historical background has been included for a number of fractional calculus applications and analytical results; for instance, refer to [10][11][12][13][14][15][16][17][18][19][20]. It has been noted that most of the studies conducted on the subject pertain to FDEs of the Caputo or Riemann-Liouville (RL) types.…”

Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals

“…The study of turbulent fluid flows, control theory, blood flow through biological tissues, porous media, and signal and image processing, among other fields, have all benefited greatly from the use of fractional calculus. The recent study on fractional calculus, including theory and applications, can be found in [1][2][3][4][5][6][7][8][9][10][11][12][13]. Their research is especially pertinent since coupled systems with fractional differential equations are used to address a wide range of real-world problems.…”

An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

“…Since theoretical findings are used to achieve a deep understanding for the fractional models, a large number of mathematicians have also assigned their focus on studying the existence aspects of solutions for several structures of fractional equations by means of different techniques and methods. For instance, see [3][4][5][6][7][8][9][10].…”