Abstract
In this paper, we prove the existence and uniqueness of solutions for a singular fractional differential equation boundary value problem with p-Laplacian operator. The main results of this paper are obtained by constructing the monotone iterative sequences of upper and lower solutions and applying the comparison result. Finally, we also provide an illustrative example in support of the existence theorem. Our results generalize some related results in the literature.
Highlights
The fractional calculus and its varied applications in many fields of science and engineering have gained much attention and developed rapidly in recent decades
Fractional differential equations have been used in the mathematical modeling of process in physics, chemistry, aerodynamics, polymer rheology, fluid flow phenomena, wave propagation, signal theory, electrical circuits, control theory and viscoelastic materials etc
Many research papers have appeared concerning the existence of solutions for the initial or boundary value problems of fractional differential equations; see [8,9,10,11,12,13,14,15,16,17,18,19]
Summary
The fractional calculus and its varied applications in many fields of science and engineering have gained much attention and developed rapidly in recent decades. Many research papers have appeared concerning the existence of solutions for the initial or boundary value problems of fractional differential equations; see [8,9,10,11,12,13,14,15,16,17,18,19]. Some papers considered recently fractional boundary value problems with p-Laplacian [12,13,14, 20, 21], and the upper and lower method and the monotone iterative technique are used in [12,13,14]. [11] considered the following fractional differential equations with nonlinear boundary conditions:
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