Abstract
We solve a coupled system of nonlinear fractional differential equations equipped with coupled fractional nonlocal non-separated boundary conditions by using the Banach contraction principle and the Leray–Schauder fixed point theorem. Finally, we give examples to demonstrate our results.
Highlights
1 Introduction In last few years, some physical phenomena were described through fractional differential equations and compared with integer order differential equations which have better results, which is why researchers of different areas have paid great attention to study fractional differential equation
Fractional differential equations arise in the mathematical modeling of systems and processes occurring in many engineering and scientific disciplines such as physics, chemistry, polymer rheology, control theory, diffusive transport akin to diffusion, electrical networks, probability, etc
In the last few decades, fractional-order differential equations equipped with a variety of boundary conditions have been studied
Summary
Some physical phenomena were described through fractional differential equations and compared with integer order differential equations which have better results, which is why researchers of different areas have paid great attention to study fractional differential equation. In the last few decades, fractional-order differential equations equipped with a variety of boundary conditions have been studied. Ahmad and Nieto [6] investigated the existence and uniqueness of solutions for an anti-periodic fractional boundary value problem cDqx(t) = f t, x(t) , t ∈ [0, T], 1 < q ≤ 2, T > 0, x(0) = –x(T), cDpx(0) = –cDpx(T), 0 < p < 1, where cDq denotes the Caputo fractional derivative of order q, f is a given continuous function.
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