Abstract
In this paper, we study a class of generalized fractional order three-point boundary value problems that involve fractional derivative defined in terms of weight and scale functions. Using several fixed point theorems, the existence and uniqueness results are obtained.
Highlights
1 Introduction Fractional calculus is the subject of studying fractional integrals and fractional derivatives, which means that the orders of integration and differentiation are not integers but non-integers, and even complex numbers
5 Conclusion remark The existence results of generalized fractional boundary value problem are discussed in this paper by using several fixed point theorems
The generalized fractional derivative is defined upon a weight function and a scale function, which contains many fractional derivatives in the literature as special cases
Summary
Fractional calculus is the subject of studying fractional integrals and fractional derivatives, which means that the orders of integration and differentiation are not integers but non-integers, and even complex numbers. In [ ], the existence and multiplicity of positive solutions for a nonlinear FBVP with two-point boundary condition are studied. In , a new class of generalized fractional integrals and derivatives defined by using a weight function and a scale function was introduced in [ ]. We will apply some fixed point theorems to study the existence and uniqueness results of this generalized fractional boundary value problem.
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