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An analysis for Klein–Gordon equation using fractional derivative having Mittag–Leffler‐type kernel
Author(s) -
Kumar Amit,
Baleanu Dumitru
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7122
Subject(s) - mathematics , fractional calculus , uniqueness , kernel (algebra) , mittag leffler function , type (biology) , convergence (economics) , mathematical analysis , integral equation , work (physics) , pure mathematics , ecology , biology , economics , mechanical engineering , engineering , economic growth
Within this paper, we present an analysis of the fractional model of the Klein–Gordon (K‐G) equation. K‐G equation is considered as one of the significant equations in mathematical physics that describe the interaction of soliton in a collision less plasma. In a novel aspect of this work, we have used the latest form of fractional derivative (FCs), which contains the Mittag–Leffler type of kernel. The homotopy analysis transform method (HATM) is being taken to solve the fractional model of the K‐G equation. A convergence study of HATM has been studied. The existence and uniqueness of the solution for the fractional K‐G equation are presented. For verifying the obtained numerical outcomes regarding accuracy and competency, we have given different graphical presentations. Figures are reflecting that a novel form of the technique is a good organization in respect of proficiency and accurateness to solve the mentioned fractional problem.