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Global Existence and Ulam–Hyers Stability of Ψ–Hilfer Fractional Differential Equations
Kishor Deoman Kucche,Jyoti Pramod Kharade 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.3
In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam–Hyers and Ulam–Hyers–Rassias stabilities of the Cauchy–type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using ε- approximated solutions. Finally, we present examples to illustrate our main results.
Pawar, N.B.,Mali, S.S.,Kharade, S.D.,Gang, M.G.,Patil, P.S.,Kim, J.H.,Hong, C.K.,Bhosale, P.N. Elsevier 2014 CURRENT APPLIED PHYSICS Vol.14 No.3
In the present paper we report structural, optical, morphological and electrical properties of thin films of MoBi<SUB>2</SUB>S<SUB>5</SUB> prepared by facile self organized arrested precipitation technique (APT) from aqueous alkaline bath. X-ray diffraction study on thin films suggests orthorhombic and rhombohedral mixed phase structure. The samples are further annealed under vacuum at 373 and 473 K. The EDS pattern shows minor loss of sulphur upto 473 K. The optical absorption in visible region shows direct allowed transition with band gap variation over 1.2-1.1 eV. Post-heat treated samples exhibit n-type electrical conductivity. SEM images show uniform distribution of spherical grains with diameter ~200 nm for as-synthesized MoBi<SUB>2</SUB>S<SUB>5</SUB> thin film. The grain size increases with annealing temperature and morphology becomes more compact due to crystallization of thin film. The surface roughness deduced from AFM, was in the range of 1.29-1.92 nm. The MoBi<SUB>2</SUB>S<SUB>5</SUB> thin films are employed for the fabrication of photoelectrochemical solar cells as all the samples exhibit strong absorption in visible to near IR region. Due to vacuum annealing it gives a significant enhancement of power conversion efficiency (η) upto 0.14% as compared to as-synthesized MoBi<SUB>2</SUB>S<SUB>5</SUB> thin film.
Novel-approach for fabrication of CdS thin films for photoelectrochemical solar cell application
Khot, Kishorkumar V.,Mali, Sawanta S.,Kharade, Rohini R.,Mane, Rahul M.,Patil, Pramod S.,Hong, Chang Kook,Kim, Jin Hyeok,Heo, Jaeyeong,Bhosale, Popatrao N. Springer-Verlag 2014 Journal of materials science. Materials in electro Vol.25 No.12
Symmetric supercapacitor: Sulphurized graphene and ionic liquid
Shaikh, Jasmin S.,Shaikh, Navajsharif S.,Kharade, Rohini,Beknalkar, Sonali A.,Patil, Jyoti V.,Suryawanshi, Mahesh P.,Kanjanaboos, Pongsakorn,Hong, Chang Kook,Kim, Jin Hyeok,Patil, Pramod S. Elsevier 2018 JOURNAL OF COLLOID AND INTERFACE SCIENCE - Vol.527 No.-
<P><B>Abstract</B></P> <P>Symmetric supercapacitor is advanced over simple supercapacitor device due to their stability over a large potential window and high energy density. Graphene is a desired candidate for supercapacitor application since it has a high surface area, good electronic conductivity and high electro chemical stability. There is a pragmatic use of ionic liquid electrolyte for supercapacitor due to its stability over a large potential window, good ionic conductivity and eco-friendly nature. For high performance supercapacitor, the interaction between ionic liquid electrolyte and graphene are crucial for better charge transportation. In respect of this, a three-dimensional (3D) nanoporous honeycomb shaped sulfur embedded graphene (S-graphene) has been synthesized by simple chemical method. Here, the fabrication of high performance symmetric supercapacitor is done by using S-graphene as an electrode and [BMIM-PF<SUB>6</SUB>] as an electrolyte. The particular architecture of S-graphene benefited to reduce the ion diffusion resistance, providing the large surface area for charge transportation and efficient charge storage. The S-graphene and ionic liquid-based symmetric supercapacitor device showed the large potential window of 3.2 V with high energy density 124 Wh kg<SUP>−1</SUP> at 0.2 A g<SUP>−1</SUP> constant applied current density. Furthermore, this device shows good cycling performance (stability) with a capacitive retention of 95% over 20,000 cycles at a higher current density of 2 A g<SUP>−1</SUP>.</P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>
Kondalkar, Vijay V.,Mali, Sawanta S.,Kharade, Rohini R.,Khot, Kishorkumar V.,Patil, Pallavi B.,Mane, Rahul M.,Choudhury, Sipra,Patil, Pramod S.,Hong, Chang K.,Kim, Jin H.,Bhosale, Popatrao N. The Royal Society of Chemistry 2015 Dalton Transactions Vol.44 No.6
<P>Herein, we report honeycomb nanostructured single crystalline hexagonal WO<SUB>3</SUB> (h-WO<SUB>3</SUB>) thin films in order to improve electrochromic performance. In the present investigation, honeycomb nanostructured WO<SUB>3</SUB> with different unit size and nanowire array with highly nanocrystalline frameworks have been synthesized <I>via</I> a hydrothermal technique. The influence of hydrothermal reaction time on the honeycomb unit cells, crystallite size, lithium ion diffusion coefficient and switching time for coloration/bleaching were studied systematically. The electrochromic study reveals that the honeycomb unit cell size has a significant impact on the electrochromic performance. Small unit cells in the honeycomb lead to large optical modulation and fast switching response. A large optical modulation in the visible spectral region (60.74% at <I>λ</I> = 630 nm) at a potential of −1.2 V with fast switching time (4.29 s for coloration and 3.38 s for bleaching) and high coloration efficiency (87.23 cm<SUP>2</SUP> C<SUP>−1</SUP>) is observed in the honeycomb WO<SUB>3</SUB> thin films with a unit cell diameter of 1.7 μm. The variation in color on reduction of WO<SUB>3</SUB> with applied potential has been plotted on an <I>xy</I>-chromaticity diagram and the color space coordinate shows the transition from a colorless to deep blue state.</P> <P>Graphic Abstract</P><P>Honeycomb nanostructured single crystalline hexagonal WO<SUB>3</SUB> (h-WO<SUB>3</SUB>) thin films in order to improve electrochromic performance. <IMG SRC='http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/image/GA?id=c4dt02953d'> </P>
N.B. Pawar,S.S. Mali,S.D. Kharade,M.G. Gang,P.S. Patil,김진혁,C.K. Hong,P.N. Bhosale 한국물리학회 2014 Current Applied Physics Vol.14 No.3
In the present paper we report structural, optical, morphological and electrical properties of thin films of MoBi2S5 prepared by facile self organized arrested precipitation technique (APT) from aqueous alkaline bath. X-ray diffraction study on thin films suggests orthorhombic and rhombohedral mixed phase structure. The samples are further annealed under vacuum at 373 and 473 K. The EDS pattern shows minor loss of sulphur upto 473 K. The optical absorption in visible region shows direct allowed transition with band gap variation over 1.2e1.1 eV. Post-heat treated samples exhibit n-type electrical conductivity. SEM images show uniform distribution of spherical grains with diameter w200 nm for as-synthesized MoBi2S5 thin film. The grain size increases with annealing temperature and morphology becomes more compact due to crystallization of thin film. The surface roughness deduced from AFM, was in the range of 1.29e1.92 nm. The MoBi2S5 thin films are employed for the fabrication of photoelectrochemical solar cells as all the samples exhibit strong absorption in visible to near IR region. Due to vacuum annealing it gives a significant enhancement of power conversion efficiency (h) upto 0.14% as compared to as-synthesized MoBi2S5 thin film.