Existence and multiplicity of positive solutions for elliptic systems
Nonlinear Analysis: Theory, Methods & Applications
Computers & Mathematics with Applications
Continuity of solutions to discrete fractional initial value problems
Computers & Mathematics with Applications
Foundations of nabla fractional calculus on time scales and inequalities
Computers & Mathematics with Applications
Discrete-time fractional variational problems
Signal Processing
Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
Computers & Mathematics with Applications
Principles of delta fractional calculus on time scales and inequalities
Mathematical and Computer Modelling: An International Journal
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In this paper, we consider a system of (continuous) fractional boundary value problems given by {-D"0"^"+^@n^"^1y"1(t)=@l"1a"1(t)f(y"1(t),y"2(t)),-D"0"^"+^@n^"^2y"2(t)=@l"2a"2(t)g(y"1(t),y"2(t)), where @n"1, @n"2@?(n-1,n] for n3 and n@?N, subject either to the boundary conditions y"1^(^i^)(0)=0=y"2^(^i^)(0), for 0@?i@?n-2, and [D"0"^"+^@ay"1(t)]"t"="1=0=[D"0"^"+^@ay"2(t)]"t"="1, for 1@?@a@?n-2, or y"1^(^i^)(0)=0=y"2^(^i^)(0), for 0@?i@?n-2, and [D"0"^"+^@ay"1(t)]"t"="1=@f"1(y), for 1@?@a@?n-2, and [D"0"^"+^@ay"2(t)]"t"="1=@f"2(y), for 1@?@a@?n-2. In the latter case, the continuous functionals @f"1, @f"2:C([0,1])-R represent nonlocal boundary conditions. We provide conditions on the nonlinearities f and g, the nonlocal functionals @f"1 and @f"2, and the eigenvalues @l"1 and @l"2 such that the system exhibits at least one positive solution. Our results here generalize some recent results on both scalar fractional boundary value problems and systems of fractional boundary value problems, and we provide two explicit numerical examples to illustrate the generalizations that our results afford.