Abstract
This paper studies two classes of boundary value problems within the generalized Caputo fractional operators. By applying the fixed point result of α-ϕ-Geraghty contractive type mappings, we derive new results on the existence and uniqueness of the proposed problems. Illustrative examples are constructed to demonstrate the advantage of our results. The theorems reported not only provide a new approach but also generalize existing results in the literature.
Highlights
It has been realized that fractional calculus (FC) has played a very important role in different areas of research; see [26, 32] and the references cited therein
Fractional differential equations (FDEs) have grasped the interest of many researchers working in diverse applications [22, 39]
Inspired by the above results and motivated by the recent evolutions in κ-fractional calculus, in this paper, we apply the fixed point (FP) technique of α-ψ-GC type mappings to investigate the existence of positive solutions for the following fractional BVPs:
Summary
It has been realized that fractional calculus (FC) has played a very important role in different areas of research; see [26, 32] and the references cited therein. The investigation of existence and uniqueness of solutions to several types of fractional (impulsive, functional, evolution, etc.) differential equations is the main topic of applied mathematics research. For the purpose of completeness, we refer thereafter to some relevant papers that deal with the existence of positive solutions involving classical Ca and RL derivatives.
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