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A discussion on the existence and uniqueness analysis for the coupled two-term fractional differential equations. (English) Zbl 1506.34021

In the last few decades, the principles of fractional calculus have played the important role in mathematics and physics. Differential equations of integer order cannot suit some physical problems, but these kind of problems fit in the differential equations of fractional order. Recently, many researchers have done valuable performances in electromagnetic, control theory, signal, porous media, viscoelasticity, biological, engineering problems, image processing, fluid flow, diffusion, theology, etc. In some circumstances, to solve the equation containing more than one derivative term are necessary. This type of equation is known as a multiterm fractional differential equation.
In the paper a nonlocal boundary value problem of coupled nonlinear fractional differential system with two-term fractional derivative is studsied. The existence and uniqueness results for the two-term fractional systems are esitablished by using the fixed point theories. To to illustrate the application of the main results obtained in the paper, two examples are provided.

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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