[PDF] Top 20 On the existence of nonnegative solutions for a class of fractional boundary value problems

... the fractional derivative and fractional dif- ferential equations, written by Miller and Ross [4], Podlubny [5] and others ...of fractional order differential equa- tions have been discussed in ... See full document

... Fractional boundary value problems (FBVPs) appear in many of these ...the existence result of a solution and to study the behavior of the solution of FBVPs have be- come more and more ... See full document

... Remark 4. Notice that the hypotheses in Theorem 3 are invariant by continuous per- turbation. More precisely, if f(t, 0) = 0 for any t Î [0, 1] and f satisfies (H1) and (H2) of Theorem 3 then g(t, x) = a(t) + f(t, x) ... See full document

... on fractional differential equations have appeared ...linear fractional equation in terms of a special function see, ...to problems of analyticity in the complex domain ...the existence of a ... See full document

... the existence of solutions for integer order differential equations with some boundary conditions; see for instance, in the vast literature on the subject, the classical books [19, 22, 27] and ... See full document

... of fractional derivatives such as ψ -Hilfer fractional derivative, Hilfer–Katugampola frac- tional derivative, and generalized proportional fractional derivative [1, 2, 12, 14–17, 23, ...-Hilfer ... See full document

... for computing the Moore-Penrose inverse of matrix is the singular value decomposition (SVD) method (see []). This method is accurate but time-intensive since it requires a large amount of computational ... See full document

... By using the Laplace transform, the kernel function is obtained. And then, by using the eigenvalue and the improved Leray-Schauder degree, the existence of the solutions to boundary value ... See full document

... the existence of solutions for multipoint boundary value problems (BVPs for short in the remaining) at nonresonance of FDEs (see ...the existence of solutions for a ... See full document

... on existence and uniqueness of boundary value problems of linear and/or nonlinear fractional equations has attracted the attention of many ...the existence and uniqueness of ... See full document

... of fractional order boundary value problems associated with p-Laplacian ...the existence of positive solutions for third order Sturm–Liouville boundary value ... See full document

... the existence of solutions for boundary value problem ...the existence of critical points for the corresponding functional, it is necessary to construct an appropriate function ... See full document

... the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques ... See full document

... the existence of positive solutions for a class of fractional multi-point boundary value problems under different resonant ...new existence results are ... See full document

... the existence of positive solutions for the above boundary value problems by utilizing a fixed point theorem in ...Several existence results for positive solutions in terms ... See full document

... the existence of nonnegative solutions for the Riemann-Liouville fractional differential equation with integral terms (E) sup- plemented with the boundary conditions (BC) which contain ... See full document

... The existence of the positive solutions to fractional boundary value problems involving the nonlinear boundary conditions is an important issue in the area of ... See full document

... It is well-known that [17,18] if the second order linear Equation (1.4) has a positive solution or nonoscillatory at ∞, then there exist two linearly independent solutions u(t) and v(t), called principal and ... See full document

... Now, we prove Theorem . by Lemma .-. and the intermediate value theorem. Proof of Theorem . It is obvious that the right-hand side of (.) is continuously de- pendent on the parameter μ, so we need to ... See full document

... the existence and multiplicity of positive solutions of the system (S)-(BC) are equivalent to the existence and multiplicity of fixed points of the operator ... See full document