Abstract
In this manuscript, we study the existence of solutions for a coupled system of nonlinear hybrid differential equations of fractional order involving Hadamard derivative with nonlocal boundary conditions. By using suitable fixed point theorems we establish sufficient conditions for the existence result. An example is provided to illustrate our main result.
Highlights
Differential Equations of Fractional Order (DEFO) gain huge attention among scientists due to the applications which are not possible with integer order ordinary or partial differential equations
The interested readers can refer to Wang et al [21], where the authors used some classical methods to analyze the Ulam–Hyers stability and proved existence results for Hadamard fractional differential equations
5 Conclusions We have presented the existence result for boundary value problems of coupled hybrid differential systems involving the Hadamard fractional derivative
Summary
Differential Equations of Fractional Order (DEFO) gain huge attention among scientists due to the applications which are not possible with integer order ordinary or partial differential equations. We define the nonhomogeneous boundary value problems of coupled hybrid fractional differential equations of Hadamard type of the function space X = C([1, e], R) of continuous real valued functions f1 : [1, e] → R. Definition 2.1 ([18]) The Hadamard fractional derivative of order β1 for a continuous function h1 : [1, ∞] → R is defined as
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