Existence results for coupled system of nonlinear differential equations and inclusions involving sequential derivatives of fractional order

Abstract

<abstract><p>In this article, we investigate new results of existence and uniqueness for systems of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order and along with new kinds of coupled discrete (multi-points) and fractional integral (Riemann-Liouville) boundary conditions. Our investigation is mainly based on the theorems of Schaefer, Banach, Covitz-Nadler, and nonlinear alternatives for Kakutani. The validity of the obtained results is demonstrated by numerical examples.</p></abstract>

Existence and Stability Results for Caputo-Type Sequential Fractional Differential Equations with New Kind of Boundary Conditions

“…e boundary value problems of fractional order, in particular, garnered much attention. See [12][13][14][15][16][17][18][19] for the most recent results on FDEs with multipoint and integral boundary conditions.…”

“…Numerous authors have also examined coupled systems of di erential equations of fractional order. ese systems naturally exist in a wide variety of real-world circumstances [19][20][21][22]. A series of papers [19,20,[23][24][25][26][27] and the sources listed therein contain some recent results on this subject.…”

“…ese systems naturally exist in a wide variety of real-world circumstances [19][20][21][22]. A series of papers [19,20,[23][24][25][26][27] and the sources listed therein contain some recent results on this subject. More recently, in [28], the authors discussed the existence and uniqueness of coupled system of nonlinear FDEs with a new kind of coupled boundary conditions speci ed by C D ϖ u(t) f(t, u(t), v(t)), t ∈ F [0, T],…”

“…In [19], authors studied the existence for a the system of nonlinear coupled Caputo-type SFDEs and inclusions subject to multipoint and fractional integral boundary conditions of the form…”

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.…”